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1. Introduction to Mathematical Logic by Alonzo Church  
Paperback: 378
Pages
(19961028)
list price: US$67.50  used & new: US$42.75 (price subject to change: see help) Asin: 0691029067 Average Customer Review: Canada  United Kingdom  Germany  France  Japan  
Editorial Review Product Description Customer Reviews (2)
a classic, but mostly useful as a historical reference
One of the classics In the introduction to the book the author defines the terms and concepts he will use in the book, with a discussion of proper names, constants and variables, functions, and sentences. He adopts the Fregian point of view that sentences are names of a particular kind. His discussion of this is rather vague however, for he does not give enough clarification of the difference between an "assertive" use of a sentence and its "nonassertive" use. Readers will have to do further reading on Frege in order to understand this distinction more clearly, but essentially what Church is saying here is that sentences are names with truth values. The existential and universal quantifiers are introduced as well. And here the author also introduces the concepts of object language and metalanguage, along with a discussion of the axiomatic method. The author distinguishes between informal and formal axiomatic methods. The modern notions of syntax and semantics are given a nice treatment here, and the di scussion is more indepth than one might get in more modern texts on mathematical logic. Chapter 1 is a detailed overview of propositional logic, being the usual formal system with three symbols, one constant, an infinite number of variables, rules on how to form wellformed formulas, and the rules of inference. The deduction theorem is proved in detail along with a discussion of the decision problem for propositional logic, with the famous truth tables due to W. Quine introduced here. The notions of consistency and completeness are briefly discussed. The discussion of the propositional calculus is continued in the next chapter where a new system of propositional calculus is obtained by dropping the constants from the first one and adding another symbol (negation). The two systems are shown to be equivalent to each other using a particular wellformed formula in the second one to replace the constant in the first. Other systems of propositional calculus are also introduced here, using the idea of primitive connectives such as disjunction, along with various rules of inference. Church also outlines an interesting propositional calculus due to J.G.P.Nicod, which assumes only one primitive connective, one axiom, and only one rule of inference (besides substitution). The author also introduces partial systems of propositional calculus, with the goal of showing just what must be added to these systems to obtain the full propositional calculus. He discusses the highly interesting and thoughtprovoking intuitionistic propositional calculus, due to A. Heyting, which is a formalization of the famous mathematical intuitionism of L.E.J. Brouwer. The system he discusses is a variant of Heyting's and he gives references to the positive solution of the decision problem for this system. The author ends the chapter with a brief discussion of how to construct a propositional calculus by employing axiom schemata. The author then moves on to what he has termed functional calculi of first order beginning in the next chapter. Called predicate calculi in today's parlance, the author first defines the pure functional calculus of first order, and shows that the theorems of the propositional calculus also follow when considered as part of this system. Free and bound variables are defined, and Church proves explicitly the consistency of this system, and the deduction theorem. The important construction of a prenex normal form of a wellformed formula is discussed, and the author shows that every wellformed formula of the functional calculus is equivalent to some wellformed formula in prenex normal form. In chapter 4, the author gives an alternative formulation of pure functional calculus of first order, wherein rules of substitution are used and axiom schemata are replaced by instances, making the number of axioms finite. The Skolem normal form of a wellformed formula is defined, which sets up a discussion of satisfiability and validity. The author then proves the Godel completeness theorem, which states that every valid wellformed formula is a theorem. This is followed by a very well written discussion of the SkolemLowenheim theorem, and an overview of the decision problem in functional (predicate) calculus. In the last chapter of the book the author considers functional (predicate) calculi of second order, which is distinguished from the first order case by allowing the variables to range over what its predicates and subjects represent. In secondorder functional calculus, propositional and predicate variables can have bound occurrences. The author discusses the elimination problem and consistency for secondorder predicate calculus, and gives a proof of the (Henkin) completeness theorem. A fairly detailed discussion of a logical system for elementary number theory is given, but the treatment involves notation that is somewhat clumsy and the discussion is difficult to follow. ... Read more 
2. Elementary topics in mathematical logic by Alonzo Church  
Unknown Binding:
Pages
(1959)
Asin: B0007ENT66 Canada  United Kingdom  Germany  France  Japan  
3. Logic, Meaning and Computation : Essays in Memory of Alonzo Church (Synthese Library, 305) by Michael Zeleny  
Hardcover: 642
Pages
(20011201)
list price: US$291.00  used & new: US$219.95 (price subject to change: see help) Asin: 140200141X Canada  United Kingdom  Germany  France  Japan  
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4. Autobiography of A. C. Morehouse, an itinerant minister of the New York and New York east conferences of the Methodist Episcopal church by Alonzo Church Morehouse  
Paperback: 344
Pages
(20100730)
list price: US$32.75  used & new: US$23.55 (price subject to change: see help) Asin: 1176431420 Canada  United Kingdom  Germany  France  Japan  
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5. Sketches of The New Jersey Historical Society by Alonzo Church  
Paperback: 44
Pages
(20091216)
list price: US$16.99  used & new: US$16.99 (price subject to change: see help) Asin: 1117479137 Canada  United Kingdom  Germany  France  Japan  
6. Introduction to Mathematical Logic / Volume I by Alonzo Church  
Hardcover:
Pages
(1962)
Asin: B0045VNTEO Canada  United Kingdom  Germany  France  Japan  
7. The Calculi of Lambda Conversion. (AM6) (Annals of Mathematics Studies) by Alonzo Church  
Paperback: 77
Pages
(19850101)
list price: US$39.95  used & new: US$31.95 (price subject to change: see help) Asin: 0691083940 Canada  United Kingdom  Germany  France  Japan  
8. Die These von Church: Zur erkenntnistheoretischen und sprachphilosophischen Bedeutung der Rekursionstheorie (European university studies. Series I, German language and literature) (German Edition) by KlausDieter Schulz  
Unknown Binding: 318
Pages
(1997)
Isbn: 3631309392 Canada  United Kingdom  Germany  France  Japan  
9. Biography  Church, Alonzo (19031995): An article from: Contemporary Authors by Gale Reference Team  
Digital: 4
Pages
(20020101)
list price: US$9.95  used & new: US$9.95 (price subject to change: see help) Asin: B0007SHKKS Canada  United Kingdom  Germany  France  Japan  
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10. American Logicians: Alonzo Church, Charles Sanders Peirce, Raymond Smullyan, Haskell Curry, George Boolos, Clarence Irving Lewis, John Corcoran  
Paperback: 202
Pages
(20100914)
list price: US$28.66  used & new: US$22.93 (price subject to change: see help) Asin: 1155847415 Canada  United Kingdom  Germany  France  Japan  
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11. University of California, Los Angeles Faculty: Bertrand Russell, Alonzo Church, Alan Kay, Fm2030, Paul Pimsleur, Abraham Robinson  
Paperback: 1084
Pages
(20100914)
list price: US$110.56  used & new: US$110.55 (price subject to change: see help) Asin: 115728101X Canada  United Kingdom  Germany  France  Japan  
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12. CHURCH, ALONZO(19031995): An entry from Gale's <i>Encyclopedia of Philosophy</i> by C. Anderson  
Digital: 3
Pages
(2006)
list price: US$4.90  used & new: US$4.90 (price subject to change: see help) Asin: B001SCJLVI Canada  United Kingdom  Germany  France  Japan  
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13. Alonzo Church: An entry from Gale's <i>Science and Its Times</i> by Judson Knight  
Digital: 2
Pages
(2000)
list price: US$2.90  used & new: US$2.90 (price subject to change: see help) Asin: B0027UWW1Q Canada  United Kingdom  Germany  France  Japan  
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14. Burials at Princeton Cemetery: Kurt Gödel, John Von Neumann, Grover Cleveland, Aaron Burr, Alonzo Church, Eugene Wigner, Jonathan Edwards  
Paperback: 280
Pages
(20100915)
list price: US$35.91  used & new: US$27.29 (price subject to change: see help) Asin: 1155330226 Canada  United Kingdom  Germany  France  Japan  
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15. What is the church? by Alonzo TreÌvier Jones  
Unknown Binding: 176
Pages
(1998)
Isbn: 0927022346 Canada  United Kingdom  Germany  France  Japan  
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16. MODERN LOGIC: SINCE GÖDEL: CHURCH: An entry from Gale's <i>Encyclopedia of Philosophy</i> by Bede Rundle  
Digital: 2
Pages
(2006)
list price: US$3.90  used & new: US$3.90 (price subject to change: see help) Asin: B001SCJSHK Canada  United Kingdom  Germany  France  Japan  
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17. Tables showing the contents of the several volumes comprising the Annals of Congress: Congressional debates, Congressional globe, Congressional record, ... and succession of Supreme court justices by Alonzo Webster Church  
Paperback: 56
Pages
(18920101)
list price: US$9.99  used & new: US$9.99 (price subject to change: see help) Asin: B00385X1TQ Canada  United Kingdom  Germany  France  Japan  
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18. Introduction to Mathemaical Logic, Volume I by Alonzo Church  
Hardcover:
Pages
(1956)
Asin: B003XL9DWO Canada  United Kingdom  Germany  France  Japan  
19. Introduction to mathematical logic. Volume I. by Alonzo Church  
Unknown Binding: 378
Pages
(19560101)
Asin: B000WTKD3I Canada  United Kingdom  Germany  France  Japan  
20. Introduction to Mathematical Logic by Alonzo. Church  
Hardcover:
Pages
(19700101)
Asin: B00350HLI6 Canada  United Kingdom  Germany  France  Japan  
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