21. An Elementary Introduction To Logic And Set Theory: Methods Of Proof An axiomatic system for sentential and predicate logic is somewhatarbitrary to set up. One scheme might take as an axiom or rule http://matcmadison.edu/alehnen/weblogic/logproof.htm

IV. Methods of Proof Formal Proof Informal Proof Conditional Proof Indirect Proof ... Mathematical Induction Formal Proof A Formal Proof is a derivation of a theorem that consists of a finite sequence of well-formed formulas. Every sentence in this sequence is either an axiom, an identified premise (a statement of "fact" that is not an axiom of the formal system), or follows from previous statements by the rules of inference of the system. The only "allowed moves" in a derivation are those "sanctioned" by the axiomatic system. If we accept the rules and axioms but nevertheless doubt the conclusions of a proof, the fault must lie in the validity of the premises. An axiomatic system for sentential and predicate logic is somewhat arbitrary to set up. One scheme might take as an axiom or rule of inference what another scheme derives as a theorem from a slightly different set of axioms or rules of inference. In these notes we will designate as A an axiomatic system for sentential and predicate logic which has the following rules of inference. The statement preceded by the is the well-formed formula that follows from earlier well-formed formulas by the stated rule of inference. The ellipsis is used to stand for possible steps in the derivation before or between the well-formed formulas required for the inference.

22. An Elementary Introduction To Logic And Set Theory: Overview http://matcmadison.edu/alehnen/weblogic/logover.htm

I. Overview The English word logic comes from the Greek word "logos" usually translated as "word", but with the implication of an underlying structure or purpose. Hence its use as a synonym for God in the New Testament Gospel of John . Logic is often defined as the process of "correct" reasoning. A more precise definition might be the study of the structures of arguments that guarantees correct or true conclusions from correct or true premises. There are generally speaking two "kinds" of logic: deductive and inductive. Inductive logic is the body of methods used to generate "correct" conclusions based on observation or data. It is the type of reasoning used in the natural sciences and statistics where general principles are "inferred" from many particular facts. The use of the methods of inductive logic always carries with it the risk of incorrect generalizations, so that the validity of this kind of argument is essentially probabilistic in nature. We will consider this type of reasoning later this semester in the Probability Unit. Deductive logic is the type of reasoning used in mathematics where we start from general principles and derive from these principles particular facts and relationships. Deductive logic usually denotes the process of proving true statements (

23. 03E: Set Theory From Dave Rusin's "Known Math" collection.Category Science Math Logic and Foundations Set Theory...... ISBN 0444-86839-9; A brief but comprehensive overview Notes on logic and set theory ,by PT Johnstone, Cambridge University Press, Cambridge-New York, 1987. http://www.math.niu.edu/~rusin/known-math/index/03EXX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 03E: Set theory Introduction Naive set theory considers elementary properties of the union and intersection operators Venn diagrams, the DeMorgan laws, elementary counting techniques such as the inclusion-exclusion principle, partially ordered sets, and so on. This is perhaps as much of set theory as the typical mathematician uses. Indeed, one may "construct" the natural numbers, real numbers, and so on in this framework. However, situations such as Russell's paradox show that some care must be taken to define what, precisely, is a set. However, results in mathematical logic imply it is impossible to determine whether or not these axioms are consistent using only proofs expressed in this language. Assuming they are indeed consistent, there are also statements whose truth or falsity cannot be determined from them. These statements (or their negations!) can be taken as axioms for set theory as well. For example, Cohen's technique of forcing showed that the Axiom of Choice is independent of the other axioms of ZF. (That axiom states that for every collection of nonempty sets, there is a set containing one element from each set in the collection.) This axiom is equivalent to a number of other statements (e.g. Zorn's Lemma) whose assumption allows the proof of surprising even paradoxical results such as the Banach-Tarski sphere decomposition. Thus, some authors are careful to distinguish results which depend on this or other non-ZF axioms; most assume it (that is, they work in ZFC Set Theory).

24. 234293 - Logic And Set Theory, Spring2003 Technion Israel Institute of Technology. 234293 - logic and set theory, http://webcourse.technion.ac.il/234293

Technion - Israel Institute of Technology 234293 - Logic and Set Theory Spring 2003 Announcements Tirgul Hashlama 16/3 A Tirgul Hashlama of Tuesday tutorials (both 10:30-12:30 and 16:30-18:30) will be held on Sunday 16/3 at Taub 7. This tirgul will cover the material of the second tutorial. Created on 13/3/2003, 15:05:21 Submission of homeworks Until a cell for the course 234293 is openned in the first floor, please submit your assignments to the cell of course "Logic 1 - 234292". Created on 13/3/2003, 14:57:10 Home Assignment 1 HW 1 was published under "Home Assignments" folder. Submission is due to 16/3 12:00 in pairs. Created on 9/3/2003, 16:30:59 New tutorial, changes of rooms 1. A new tutorial is opened. The tutorial will be held on Tuesdays 16:30-18:30 at Taub 7. 2. Sundays tutorial is moved from Taub 1 to Taub 9. 3. The lecture hours are Wednesdays 10:30-12:30 and 15:30-16:30 at Taub 1. Created on 3/3/2003, 13:25:31 The tutorials on Monday 3/3 and Tuesday 4/3 are canceled. The tutorial on Thursday 6/3 will be held as usual. Tirgul Hashlama for Tuesday tutorial will be given on Sunday 16/3 16:30-18:30 at Taub 3.

25. Seminar On Logic And Set Theory Seminar on logic and set theory. http://www.risc.uni-linz.ac.at/courses/ss2002/logicsem/

News Library Links Sitemap ... Search Seminar on Logic and Set Theory Home Institute Research Education ... Industry Search: Date and Time Thursday, 14:00 - 15:30, UFO, Hagenberg. First meeting: 14.3.2002 About the Seminar The goal of the seminar is to gain more insight into foundational aspects of set theory, especially axiomatic, model theoretic, and constructive ones. Talks J. Schicho Sheaf Semantics G. Kusper Various Axiomatizations of Set Theory G. Fuchsbauer Cumulative Type Hierarchy A. Craciun The Constructive Universe J. Pilnikova Easy Independence Results H. Rolletschek Large Cardinals N. Popov Transfinite Recursion F. Piroi Propositions as Types N.N. Forcing This page is maintained by Josef Schicho Last updated on May 2, 2002

26. Sets, Relations, And Functions -- Logic And Set Theory logic and set theory. Firstorder predicate logic. The combination of first-orderpredicate logic and set theory is the working horse of mathematics. http://www.risc.uni-linz.ac.at/courses/ws99/formal/slides/sets/index_31.html

Go backward to Go up to Top Go forward to Basic Idea Logic and Set Theory First-order predicate logic. Variables may represent domain objects, not predicates or functions. No quantifiers over predicates or functions. Problem: "for all predicates p , ...", "there is a function f , such that ..." First-order predicate logic over domain of sets. Domain objects are sets. May encode predicates and functions as sets. Interpret statements about sets as statements about predicates and functions. Overcome limitations of first-order predicate logic. The combination of first-order predicate logic and set theory is the working horse of mathematics. Author: Wolfgang Schreiner Last Modification: October 14, 1999

27. Introduction To Logic And Set Theory Barwise J.(ed.), Handbook of Mathematical Logic , NorthHolland, 1977. Aristotle'sLogic a/nebo Aristotelian Syllogisms. Dobrovolná cvicení. http://www.cs.cas.cz/~zuzana/teach/lst.html

Prosemináø z logiky MFF UK, ZS 02/03; viz anotace Atestace Dvì zápoètové písemky, z logiky (cca v polovinì semestru) a z teorie množin (na konci semestru), každá po 30 bodech. Ke získání zápoètu je tøeba alespoò 40 bodù. Výsledky písemek 26/27.11. a 7./8.1. Zadání 1. písemky: 26.11.( ps ps ). Zadání 2. písemky: 7.1.( ps ps ). Zadání 2. písemky L+TM: 7.1.( ps ps Výsledky opravné písemky (z logiky a teorie množin) z pondìlí 10.2.: Murín M. 12, Michalko Jakub 13. Další písemky nebudou, domluvte si konzultaci. Kontakt a konzultace Adresa: Ústav informatiky AVÈR , Pod Vodárenskou vìží 2, Praha 8 (areál AV, ze st. tramvají 10,17,24 "Ládví" smìrem doprava, nízká èervenožlutá budova, 3. patro, è. dveøí 404) Telefon: 266 05 39 21 Email: zuzana@cs.cas.cz Konzultace a zápoèty po dohodì mailem na výše uvedené adrese. Syllabus Výroková logika: jazyk VL, formule VL. Ohodnocení promìnných, sémantika logických spojek, tautologie, kontradikce, splnitelná formule. Výpoèet pravdivostní hodnoty formule v daném ohodnocení, ovìøení, zda daná formule je splnitelná, resp. tautologie. Ekvivalence formulí, (vzájemná) (ne) definovatelnost logických spojek. Algebraické vlastnosti logických spojek (idempotence, komutativita, asociativita,...), de Morganova pravidla, distributivní zákony. DNF, CNF, existence a hledání ekvivalentní formule v DNF, resp. CNF. Reprezentace n-ární bitové operace formulí. Relace vyplývání a její vlastnosti. Vìta o substituci. Dùkaz VL, dokazatelnost, axiomy a odvozovací pravidla. Vìta o dedukci. Vztah dokazatelnosti a vyplývání (bez dk).

28. Introduction To Logic And Set Theory Výsledky písemek a zápocty. Výsledky písemky z 26. a 27. 11.2002(1. sloupec), desetiminutovky z 10. 12. (2. sloupec), písemky http://www.cs.cas.cz/~zuzana/teach/v1.html

Výsledky písemek a zápoèty Výsledky písemky z 26. a 27. 11.2002 (1. sloupec), desetiminutovky z 10. 12. (2. sloupec), písemky z 7. a 8. 1. 2003 (3. sloupec), souèet (4. sloupec) a poznámka o dalším postupu (5. sloupec). Na zápoèet je tøeba alespoò 40 bodù, tolerance 5% (2 body). "Z" znamená, že zápoèet jste získal(a). "?" znamená, že se Vás ještì zeptám na nìco, co Vám v písemce nešlo. "O" znamená opravnou písemku, na kterou se mùžete tìšit v první polovinì unora (sledujte pokyny Pokud budete ještì tázáni, zvažte, zda byste spíše než 22.1. ve 14 hodin do T5 nechtìli pøijít do Ládví, napø. 23.1. od 14 do 16 hodin, nebo po dohodì i jindy. Nemuseli byste èekat, až na Vás pøijde øada. studijní skupina 40 Mruškoviè Michal Z Muller Pavol Z Murín Martin O Nìmeèek Jiøí 30.5 (L+TM) Novák Petr Z Novotný TomᚠOblas Miroslav 13 (L+TM) O Olšák Libor Z Ondreièka Matúš O Ondrejèíková Zuzana Z Ondruška Marek 35 (L+TM) Paška Pøemysl Z Pavelka Miroslav 25 (L+TM) O Pavlík Ivo Slanèík Milan O Arabadzhieva Svetlozara 6 (L+TM) O studijní skupina 39 Marko Peter Z Martínek Vladislav Z Matouš Václav Z Matoušek Jiøí 36.5 (L+TM)

29. Modal Deduction In Second-Order Logic And Set Theory - Van Benthem, D'Agostino, We investigate modal deduction through translation into standard logic and settheory. Modal Deduction in SecondOrder logic and set theory (1997) (Make http://citeseer.nj.nec.com/101820.html

Modal Deduction in Second-Order Logic and Set Theory (1997) (Make Corrections) (13 citations) Johan van Benthem, Giovanna D'Agostino, Angelo Montanari, Alberto Policriti Journal of Logic and Computation Home/Search Context Related View or download: illc.uva.nl/Public 199502.text.ps.gz wins.uva.nl/resear 199502.text.ps.gz ... L9502.text.ps.gz Cached: PS.gz PS PDF DjVu ... Help From: illc.uva.nl/Pub wallseriesall (more) From: wins.uva.nl/res wallseriesall Homepages: A.Montanari A.Policriti HPSearch (Update Links) Rate this article: (best) Comment on this article (Enter summary) Abstract: (Update) Context of citations to this paper: More ...independent of the particular modal logic under consideration: a single theorem prover may be used for any translatable modal logic. In , a set theoretic translation method (2 as P ow translation, from now on) for (poly)modal logics has been proposed, whose basic idea ...main reason of its practical usefulness. An implementation of linear T resolution is employed in a theorem prover for polymodal logics ( ) 3 T Logic Programming In this section we introduce the syntax and semantics of the deduction scheme T Logic Programming (TLP ) Cited by: More Transitive Venn diagrams with applications to the.. - Cantone, Omodeo, Ursino (2000)

30. Modal Deduction In Second-Order Logic And Set Theory - II - Van Benthem, D'Agost Modal Deduction in SecondOrder logic and set theory II (1997) (Make Corrections)(13 1995 13 Modal Deduction in Second-Order logic and set theory; Resear.. http://citeseer.nj.nec.com/38045.html

Modal Deduction in Second-Order Logic and Set Theory II (1997) (Make Corrections) (13 citations) Johan van Benthem, Giovanna D'Agostino, Angelo Montanari, Alberto Policriti Journal of Logic and Computation Home/Search Context Related View or download: wins.uva.nl/resear L9608.text.ps.gz wins.uva.nl/pub/th L9608.text.ps.gz ... 199608.text.ps.gz Cached: PS.gz PS PDF DjVu ... Help From: fermivista.math www.wins.uva.nl (more) From: illc.uva.nl/Pub wwwallpublall Homepages: A.Montanari A.Policriti HPSearch (Update Links) Rate this article: (best) Comment on this article (Enter summary) Abstract: In this paper, we generalize the set-theoretic translation method for polymodal logic introduced in [11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, defining a new set-theoretic function symbol for each new modal operator, we develop a general framework within which a number of extended modal logics can be dealt with. More precisely, we extend the basic set-theoretic translation method to weak monadic second-order logic through a suitable change in the... (Update) Context of citations to this paper: More ...independent of the particular modal logic under consideration: a single theorem prover may be used for any translatable modal logic. In , a set theoretic translation method (2 as P ow translation, from now on) for (poly)modal logics has been proposed, whose basic idea ...main reason of its practical usefulness.

31. Computer Science 3.0. Prerequisites (, 234144 DISCRETE MATHEMATICS, ), Overlapping courses234293 - logic and set theory FOR CS, 234293 - logic and set theory FOR CS. http://www.undergraduate.technion.ac.il/catalog/02304686.html

234262 - LOGIC DESIGN Lecture Tutorial Laboratory Project/Seminar Weekly hours Credit points Prerequisites: 044145 - DIGITAL SYSTEMS and 234141 - COMBINATORICS FOR CS or 234141 - COMBINATORICS FOR CS and 234145 - DIGITAL SYSTEMS Linked courses: 234118 - COMPUTER ORGANIZATION AND PROGRAMMING 234246 - GRAPH ALGORITHMS Building blocks for digital design, with and without memory. Timing considerations. Binary arithmetic and its implementation. Algorithms for speeding up arithmetic operations. Memories. Programmable logic and its implementation. Return to the faculty subjects list 234267 - DIGITAL COMPUTER ARCHITECTURE Lecture Tutorial Laboratory Project/Seminar Weekly hours Credit points Prerequisites: 044264 - SYSTEM PROGRAMMING and 234262 - LOGIC DESIGN or 234118 - COMPUTER ORGANIZATION AND PROGRAMMING and 234262 - LOGIC DESIGN Linked courses: 234119 - INTRODUCTION TO OPERATING SYSTEMS Overlapping courses: 234248 - INT. TO DIGITAL COMPUTER 236267 - DIGITAL COMPUTER ARCHITECTURE 234290 - PROJECT 1 IN COMPUTER SCIENCE Lecture Tutorial Laboratory Project/Seminar Weekly hours Credit points Intended for students in the last semester of their studies who need 0.5 credit points to complete their studies. The student will do a project under the supervision of a faculty member.

32. Set Theory And Logic At The University Of Zimbabwe HMTH037 Set Theory And Logic. Lecturer Mr D Vuma. Additional Reading PT Johnstone,Notes on logic and set theory (Cambridge University Press, 1987). http://uzweb.uz.ac.zw/science/maths/courses/hmth037.htm

HMTH037 Set Theory And Logic Lecturer: Mr D Vuma Duration :2 semester 48 lectures Aim: The course is generally viewed as two courses `Set Theory' and `Logic' on equal weighting either running concurrently or consecutively over the two semester academic year. The overall aim is to provide the final year undergraduate mathematics specialist a general introduction to the basic ideas of Logic and axiomatic Set Theory. Course Outline: LOGIC: Propositional Calculus: Axioms, Deduction theorem, Completeness and consistency. First order languages and first order theories: the tautology theorem, results concerning quantifiers, introduction rule, generalization rule, substitution rule, substitution theorem, distribution theorem, closure theorem, deduction theorem, theorem on constants. The characterization problem: reduction theorem, reduction theorem for consistency, the completeness theorem, Lindenbaum's theorem. SET THEORY: Axiomatic foundation: Russell's paradox, axioms of set theory (extensionality, emptyset, pairset, separation, powerset, unions, and infinity axioms). Revisiting classical notions: ordered pairs, Cartesian products, disjoint unions, relations, equivalence relations, classes, and partitions, functions, indexed families, structured sets.

33. MainFrame: Books On Logic purchase from amazon purchase from ibs. logic and set theory Notes.Notes on logic and set theory, PT Johnstone Johnstone72 A starter http://www.rbjones.com/rbjpub/logic/log022.htm

what is logic? What is Mathematical Logic? , J.N. Crossley et.al. This book has pace first-order logic The Language of First Order Logic , Jon Barwise and John Etchemendy A practical approach to learning logic. The book was designed for a first course in logic using the Tarki's World 4.0 software ( Logic Software from CLSI ), which comes with the book. for PC: for MAC: Methods of Logic , Willard Van Ormon Quine A lucid introductory text from one of the best. Logic and Philosophy Philosophy of Logics , Susan Haack A readable introduction with a slightly broader interpretation of "logic" than the average philosophy text. Philosophy of Logic , Willard Van Orman Quine An excellent short (109pp) introduction with the emphasis on the philosophy. Metalogic - An Introduction to the Metatheory of Standard First-Order Logic , Geoffrey Hunter An excellent second course for philosophy students who want a good technical understanding of classical first order logic. Philosophical Logic - An Introduction , Sybil Wolfram A worthwhile fairly recent introduction to the kind of problems raised by philosophical logic. Possible Worlds - an introduction to Logic and its Philosophy , Raymond Bradley and Norman Swartz A substantial (391pp) introduction with the emphasis on propositional and modal logics.

34. LOGIC, COMPUTATION AND SET THEORY LOGIC, COMPUTATION AND SET THEORY. (J1, 16/24 lectures). Cambridge UniversityPress 1988 (£22.95 paperback). PT Johnstone Notes on logic and set theory. http://www.maths.cam.ac.uk/undergrad/schedules/text/node53.html

Next: PRINCIPLES OF STATISTICS Up: No Title Previous: NONLINEAR WAVES AND INTEGRABLE LOGIC, COMPUTATION AND SET THEORY J1, 16/24 lectures) The first sixteen lectures only will be examined in Part II(A); for Part II(B), the whole schedule will be examined as a 24-lecture course. Partially ordered sets Hasse diagrams, chains, maximal elements. Chain-complete partial orders and fixed-point theorems. The axiom of choice and Zorn's lemma; applications of Zorn's lemma in mathematics. Lattices and Boolean algebras. [5] First-order logic The propositional calculus. Semantic and syntactic entailment. The deduction and completeness theorems. Applications of completeness (compactness, decidability). [3] Recursive functions Computability defined via register machines. Universal programs; recursive and recursively enumerable sets; undecidability of the halting problem. Example of an undecidable first-order theory. [5] Set theory (Part II(B) only) Set theory as a first-order theory; the axioms of ZF set theory. Well-founded relations; the recursion theorem. Mostowski's collapsing theorem. [3]

35. Logic, Computation And Set Theory The book `Notes on logic and set theory' by PT Johnstone (CUP, 1987) covers mostof the material of the course, and is suitable for preliminary reading. http://www.maths.cam.ac.uk/undergrad/courseinfo/coursesIIB/text/node10.html

Next: Probability and Measure Up: COURSES IN PART II(B) Previous: Algebraic Curves Logic, Computation and Set Theory Michaelmas term, 24 lectures The first 16 lectures of this course are also available in Part II(A).] The aim of this course is to provide you with an understanding of the logical underpinnings of the pure mathematics you have studied in the last two years. As such, it has few formal prerequisites: some familiarity with naive set theory, such as is provided by the IA Discrete Mathematics course, is helpful, but no previous knowledge of logic is assumed. On the other hand, the course has links to almost all of pure mathematics, and examples will be drawn from a wide range of subjects to illustrate the basic ideas. The course falls into three main parts, of which the first two only are examined in Part II(A). The first begins by investigating ordered structures, an important mathematical concept which is not formally dealt with elsewhere in the Tripos, and goes on to develop the notions of validity and provability in formal logic, culminating in the Completeness Theorem which asserts that these two notions coincide. The course then develops the mathematical notion of algorithmic computability, covers basic properties of the collection of computable functions, and gives examples of the distinction between decidable and undecidable problems. For Part II(B) students only, the last eight lectures of the course provide a rigorous introduction to axiomatic set theory, concluding with a brief discussion of the famous results on consistency and independence of set-theoretic axioms.

36. The Homepage Of The Helsinki Logic Group Logic Group.Category Science Math Logic and Foundations Institutions Europe...... whose elements are complex analytic functions defined in a common domain, combiningmethods of classical complex analysis with those of logic and set theory. http://www.logic.math.helsinki.fi/

The Helsinki Logic Group University of Helsinki Logiikan opetus Logic Colloquium 2003 in Helsinki Members ... Contact Info Members Members - Research Publications Links Contact Info ... Marko Djordjevic , Ph.D., finite model theory Aapo Halko , Ph.D., descriptive set theory Taneli Huuskonen , docent, model theory, set theory, logic and analysis Tapani Hyttinen , docent, stability theory, infinitary logic Juliette Kennedy , Ph.D., models of arithmetic, philosophy of mathematics Kerkko Luosto , docent, finite and infinite model theory, abstract model theory Juha Oikkonen , university lecturer, infinitary logic, nonstandard analysis , Ph.D., set theory , professor, finite model theory, abstract model theory, set theory Ph.D. students: Marta Garcia-Matos , M.Sc. Alex Hellsten , Ph.L., set theory Juha Kontinen , M.Sc., finite model theory Matti Pauna , Ph.L. Juha Ruokolainen , Ph.L. Maria Saria , M.Sc. Former members of the group can be found in the list of Ph.Ds from the Logic Group. Main Topics of Research Members - Research - Publications Links Contact Info MODEL THEORY Research topics in model theory include homogeneous model theory i.e. model (stability) theory for classes of structures that consist of all elementary submodels of a large homogeneous structure.

37. Logic And Set Theory logic and set theory. The mathematician Hermann Weyl called logic thehygiene the mathematician practices to keep his ideas healthy http://www.southalabama.edu/mathstat/personal_pages/brick/teaching/math110/logic

Logic and Set Theory The mathematician Hermann Weyl called logic "the hygiene the mathematician practices to keep his ideas healthy and strong." It is more than that. It is the very foundation of mathematics. Its precise methods allows mathematicians to avoid paradoxes and self-contradictions. Axioms and Consistency Logic starts with axioms and uses them to construct an underlying framework for all of mathematics. The basic method is that of modus ponens which is illustrated in the classic syllogism: All men are mortal. Socrates is a man. Therefore, Socrates is mortal. Formally, given the validity of an implication "A implies B" and the truth of "A", one is allowed to conclude "B". This formal approach ioccurs for the above when one rewrites the first sentence above as "if x is a man then x is mortal". Two basic desires in logic is that the axioms one starts with are reasonable and do not lead to any contradictions. Whether some axioms are reasonable is a matter of opinion. Sometimes, one has to recognize that other axiom systems are equally reasonable, as in the case of Euclidean versus non-Euclidean geometry. The matter of whether or not contradictions occur is much more subtle. If a set of axioms does not lead to any contradictions, then we call it consistent John Allen Paulos says of him:

38. MATH301 HOME PAGE MATH301 HOME PAGE. Welcome to the logic and set theory (MATH301)home page! I About MATH301. MATH301 (logic and set theory). Logic http://frey.newcastle.edu.au/~jacqui/MATH301.html

MATH301 HOME PAGE Welcome to the Logic and Set Theory (MATH301) home page! I hope that you find what you are looking for here. You are visitor number MATH301 is taught at the Callaghan Campus. For more information about the course see me, Jacqui Ramagge , Room V127, Extension 5545, e-mail address jacqui@maths.newcastle.edu.au Contents About MATH301 Problem List Text books Lectures ... Assessment About MATH301 MATH301 (Logic and Set Theory) We shall see that set theory is at the heart of the description of the natural, rational and real numbers. Indeed, in many ways this course can be thought of as a study of the nature of infinity. Many logical paradoxes arise in the context of infinite sets. We will discuss the axiom of choice and related statments such as Zorn's Lemma. For more information about MATH301, please contact Jacqui Ramagge , Extension 5545, Room V127, or see the subject description You can change courses up until Tuesday 31st March without incurring HECS Click here to return to top of document or Click here to return to contents.

39. Set Theory Logic Book title Lectures in logic and set theory . . . . . . () Topics inMathematics Logic Set Theory The Alonzo Church Archive ADD. http://www.microrevue.com/mike-modano-photo.htm

40. Untitled logic and set theory Qualifying Examination Syllabus A good mathematical presentation of set theory. Little explicit use of firstorder logic. http://www.lehigh.edu/~math/logic.html

LOGIC AND SET THEORY Qualifying Examination Syllabus First-order logic. Propositional logic: provability, truth tables, consistency, compactness, completeness. First-order predicate logic: syntax and semantics. Deduction systems and formal proofs. Consistency, completeness and decidability of theories the methods of elimination of quantifiers, the Ehrenfeucht-Fraisse Test, and Vaught's Test. Godel's Completeness Theorem. The Henkin proof of a proof using consistency properties. The Compactness Theorem and its application. Elementary model theory. Elementary substructures and the Lowenheim-Skolem-Tarski Theorem. Godel's Incompleteness Theorem. Applications to undecidable theories. Set Theory. Axiomatic set theory. The systems ZF and GB. Relations between sets and classes. Principles of transfinite induction and recursion, and applications. The definitions of cardinal and ordinal numbers. Cardinal and ordinal arithmetic with and without the Generalized Continuum Hypothesis. The Axiom of Choice and its equivalents.

Page 2     21-40 of 79    Back | 1  | 2  | 3  | 4  | Next 20