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 Skolem Thoralf:     more detail

1. Skolem
Translate this page skolem thoralf Albert norvégien, 1887-1963 Professeur à l'universitéd'Oslo. Outre la théorie des nombres (équations diophantiennes
http://www.sciences-en-ligne.com/momo/chronomath/chrono1/Skolem.html
 SKOLEM Thoralf Albert Ackermann ou non. ZF ou ZFC ( Zermelo Fraenkel -axiome du choix ou de Zermelo : Ramanujan Bernays

2. Skolem
Thoralf Skolem developed the concept of primitive recursion and used recursivefunctions as a means of avoiding the socalled paradoxes of the infinite.
http://www.geocities.com/cyberdiction/skolem.htm
 Skolem the Pioneer Thoralf Skolem developed the concept of primitive recursion and used recursive functions as a means of avoiding the so-called paradoxes of the infinite. Primitive recursive functions may only use a simple form of recursion. In particular, the recursion must be guaranteed to terminate. General recursive functions, which don't have a decremental restriction, are more powerful than primitive recursive functions. Skolem extended work by Löwenheim (1915) to give the Löwenheim- Skolem theorem, which states that if a theory has a model then it has a countable model. From 1933 he did pioneering work in metalogic and constructed a nonstandard model of arithmetic. Nordic Logic Journal by Herman Ruge Jervell Skolem may have considered Diophantine equations and logic as one subject. Let me indicate a little speculatively how Skolem's thought might have been. The theory of Diophantine equations considers questions about satisfiability of equations like 4x^3y^4 + 3y^3 -13z^5 = This is really not far from questions about satisfiability of logical statements. A statement can be seen as a "Diophantine equation" where we have

3. The US Bridge
Logic Colloquium ESSLLI Other Logicians Turing Alan MathisonTarski Alfred skolem thoralf Peirce Charles Sanders LukasiewiczJan
http://www.theusbridge.com/MLM_4_MLM_3_Science_&_Technology_Math.html_Logic.html
 Home Advanced Search Home Math ... Logic You are in USA Search Go to Web Matches Software Proof Assistants Coq Other Other Research Groups Research Fields Temporal Logic Substructural Logics

4. Logika DVOUOBOROVÁ LOGIKA
Logika, DVOUOBOROVÁ LOGIKA. vzorový pruchod studiem. skolem thoralfSkolem (18871963). PRVNÍ CYKLUS. Nr. Název \ semestry, 1. 2. 3. 4.
http://logika.ff.cuni.cz/newpages/czech/logika2obor.htm
Thoralf Skolem
##### PRVNÍ CYKLUS
Nr. Základy matematické analýzy 2+1 Zk Teorie mnoin 2+1 Zk 1+1 Zk Programování 2+1 Z 1+1 Zk Logika I 2+1 Z 1+1 Z,Zk Algebra I 1+1 Zk Teorie algoritmù 1+1 Z 1+1 Zk Pravdìpodobnost a matematická statistika 2+2 Zk Základy filozofické logiky 2+0 Zk 1. svetovy jazyk 2. svetovy jazyk Dejiny filosofie celkem hodin(bodu)
##### DRUHÝ CYKLUS
Nr. Algebra II 1+1 Zk Dejiny logiky 2+0 Z Logika II 2+0 Zk Informatika a teorie pocitacu 1+1 Zk Vyberova prednaska C 2+0 Kv 2+0 Kv 2+0 Kv Teorie racionalniho usuzovani 2+0 Z Logické programování 0+2 Zk Vypoctova slozitost I 2+0 Zk Vyberova prednaska A 2+0 Kv Neklasicke logiky I 2+0 Zk Logika III 2+0 Zk Vyberova prednaska A 2+0 Kv Intenzionalni logiky 2+0 Z Vyberova prednaska A 2+0 Kv Diplomovy seminar 0+2 Z celkem hodin(bodu)
##### Poznamky
1 Plati pro nastupni rocnik 93 a pozdejsi 2 Plati pro nastupni rocnik 92 a drivejsi
##### Navaznost predmetu.
Prednaska Logika II (neuplnost a nerozhodnotelnost) a Logika III (teorie modelu) jsou navzajem nezvisle a obe navazuji na Logiku I (vyrokovy a predikatovy pocet). Logika II navic silne navazuje Teorii algoritmu. Logika III navazuje take na prednasky z algebry. Vypoctova slozitost I a II navazuji na Teorii algoritmu. I jine prednasky 2. cyklu vyuzivaji nektere poznatky z 1. cyklu.
##### Souborna postupova zkouska.

5. Skolem
Biography from MacTutor History of mathematics archive.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Skolem.html
##### Born: 23 May 1887 in Sandsvaer, Norway Died: 23 March 1963 in Oslo, Norway
Click the picture above
to see a larger version Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
Thoralf Skolem worked on Diophantine equations , mathematical logic, group theory , lattice theory and set theory. In 1912 he produced a description of a free distributive lattice. He made refinements to Zermelo 's axiomatic set theory, publishing work in 1922 and 1929. Skolem extended work by He also developed the theory of recursive functions as a means of avoiding the so-called paradoxes of the infinite.
Article by: J J O'Connor and E F Robertson Click on this link to see a list of the Glossary entries for this page List of References (6 books/articles) Mathematicians born in the same country Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
History Topics

Societies, honours, etc.
... Anniversaries for the year JOC/EFR December 1996 School of Mathematics and Statistics
University of St Andrews, Scotland
http://www-history.mcs.st-andrews.ac.uk/history/References/Skolem.html

6. References For Skolem
References for thoralf skolem. G Gjone, Über Leben und Werk von thoralf skolem, Contributionsto the history, philosophy and methodology of mathematics, Wiss.
http://www-gap.dcs.st-and.ac.uk/~history/References/Skolem.html
##### References for Thoralf Skolem
• Biography in Dictionary of Scientific Biography (New York 1970-1990). Articles:
• E Fenstadt, Thoralf Albert Skolem in Memoriam, Nordisk Mathematisk Tidsskrift
• Contributions to the history, philosophy and methodology of mathematics, Wiss. Z. Greifswald, Ernst- Moritz- Arndt- Univ. Math.-Natur. Reihe
• W Ljunggren, Thoralf Albert Skolem in memoriam, Math. Scand.
• T Nagell, Thoralf Skolem in Memoriam, Acta Mathematica (1963), i-xi.
• S Selberg, Thoralf Albert Skolem (Norwegian), Norske Vid. Selsk. Forh. (Trondheim) Main index Birthplace Maps Biographies Index
History Topics
... Anniversaries for the year
JOC/EFR December 1996 School of Mathematics and Statistics
University of St Andrews, Scotland
http://www-history.mcs.st-andrews.ac.uk/history/References/Skolem.html
• 7. References
Translate this page Conclusion. References. skolem, thoralf. 1919a. Untersuchungen überdie pp. 67-101. skolem, thoralf. 1920a. Logisch-kombinatorische
http://www.hf.uio.no/filosofi/njpl/vol1no2/pioneer/node14.html
Next: Up: Thoralf Skolem: Pioneer of Previous: 13. Conclusion
##### References
Skolem, Thoralf. 1919a.
Untersuchungen über die Axiome des Klassenkalküls und über Produktations- und Summationsprobleme, welche gewisse Klassen von Aussagen betreffen.
Skrifter utgit av Videnskabsselskapet i Kristiania
Reprinted in Skolem , pp. 67-101.
Skolem, Thoralf. 1920a.
Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit und Beweisbarkeit mathematischen Sätze nebst einem Theoreme über dichte Mengen.
Skrifter utgit av Videnskabsselskapet i Kristiania, I. Matematisk-naturvidenskabelig klasse , 4, pp. 1-36.
Reprinted in Skolem , pp. 103-136.
Skolem, Thoralf. 1922a.
Über ganzzahlige Lösungen einer Klasse unbestimmter Gleichungen.
Norsk Matematisk Forenings skrifter , series 1, no. 12.
Skolem, Thoralf. 1922b.
Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre.
In Matematikerkongressen i Helsingfors 4-7 juli 1922, Den femte skandinaviska matematikerkongressen, Redogörelse , pp. 217-232. Akademiska Bokhandeln, Helsinki.
Reprinted in Skolem , pp. 137-152.

8. Albert Thoralf Skolem
Albert thoralf skolem Seite aus einem deutschsprachigen OnlinePhilosophenlexikon. Der norwegische Mathematiker und Logiker Albert thoralf skolem hat zu vielen Gebieten der mathematischen Grundlagen
http://www.philosophenlexikon.de/skolem.htm
Begriffe Abaelard - Ayer

Cabanis - Czezowski

Ebbinghaus - Ewald
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##### Albert Thoralf Skolem (1887 - 1963)

9. Skolem
Biography from MacTutor History of mathematics archive.Category Science Math History People skolem, thoralf......Albert thoralf skolem. thoralf skolem worked on Diophantine equations,mathematical logic, group theory, lattice theory and set theory.
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Skolem.html
##### Born: 23 May 1887 in Sandsvaer, Norway Died: 23 March 1963 in Oslo, Norway
Click the picture above
to see a larger version Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
Thoralf Skolem worked on Diophantine equations , mathematical logic, group theory , lattice theory and set theory. In 1912 he produced a description of a free distributive lattice. He made refinements to Zermelo 's axiomatic set theory, publishing work in 1922 and 1929. Skolem extended work by He also developed the theory of recursive functions as a means of avoiding the so-called paradoxes of the infinite.
Article by: J J O'Connor and E F Robertson Click on this link to see a list of the Glossary entries for this page List of References (6 books/articles) Mathematicians born in the same country Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
History Topics

Societies, honours, etc.
... Anniversaries for the year JOC/EFR December 1996 School of Mathematics and Statistics
University of St Andrews, Scotland
http://www-history.mcs.st-andrews.ac.uk/history/References/Skolem.html

10. Thoralf Albert Skolem 1887-1963: A Biographical Sketch
thoralf Albert skolem 18871963 A Biographical Sketch Originally published as ``thoralf Albert skolem in Memoriam'', in Th. skolem Selected Works in Logic, edited by Jens E.
http://www.hf.uio.no/filosofi/njpl/vol1no2/skobio
Next: Thoralf Albert Skolem Up: Contents
##### Thoralf Albert Skolem 1887-1963: A Biographical Sketch
Originally published as ``Thoralf Albert Skolem in Memoriam'', in Th. Skolem: Selected Works in Logic , edited by Jens E. Fenstad (Universitetsforlaget, Oslo 1970). Reprinted here with minor language changes.
Postscript, compressed: skobio-ps.zip (45987 bytes)
TeX DVI: skobio.dvi (28336 bytes)
TeX DVI, compressed: skobio-dvi.zip (13593 bytes) Nordic Journal of Philosophical Logic, Vol. 1, No. 2, pp. 99106.

11. References
Translate this page skolem, thoralf. 1910. H. Weyl. Über die Definitionen der mathematischenGrundbegriffe. 89-90. Review of Weyl 1910. skolem, thoralf. 1920.
http://www.hf.uio.no/filosofi/njpl/vol1no2/skogod/node2.html
Next: Up: Skolem and Gödel Previous: Skolem and Gödel
##### References
Boos, William. Jul. 1992.

Typescript.

, 2, p. 3.
Reprinted in , pp. 240-242.

, 4, p. 385.
Reprinted in , p. 262.

, 40, pp. 433-443.
Reprinted in , pp. 306-326.
Besprechung von ``Ein kombinatorischer Satz mit Anwendung auf ein logisches Entscheidungsproblem''.
, 7, pp. 97-98.
Reprinted in , p. 372.

, 2, p. 3. Reprinted in , pp. 378-380.
, 10, p. 49. Reprinted in , p. 384.
Collected Works, edited by Solomon Feferman , vol. 1. Oxford University Press, New York.
Goldfarb, Warren D. 1971.
Review of Skolem 1970 Journal of Philosophy , 68, pp. 520-530.
Goldfarb, Warren D. 1979.
Logic in the twenties: The nature of the quantifier. Journal of Symbolic Logic , 44, pp. 351-368.
van Heijenoort, Jean (ed.). 1967.
Harvard University Press, Cambridge, Mass.
Skolem, Thoralf. 1910.
, 41, pp. 89-90. Review of Weyl 1910
Skolem, Thoralf. 1920.
Skrifter utgit av Videnskabsselskapet i Kristiania, I. Matematisk-naturvidenskabelig klasse , 4, pp. 1-36. Reprinted as 1920a in Skolem 1970 , pp. 103-136.

12. Skolem, Thoralf Albert
skolem, thoralf Albert (18871963). Norwegian mathematician who didimportant work on Diophantine equations and who helped to provide
http://www.cartage.org.lb/en/themes/Biographies/MainBiographies/S/Skolem/1.html
 Skolem, Thoralf Albert Norwegian mathematician who did important work on Diophantine equations and who helped to provide the axiomatic foundations for set theory in logic. Skolem was born at Sandsvaer and educated at Oslo, where he became professor 1938. He wrote 182 scientific papers, but they remained largely unread, partly because they were written in Norwegian. Before such subjects as model theory, recursive function theory, and axiomatic set theory had become separate branches of mathematics, he introduced a number of the fundamental notions that gave rise to them.

 13. Directory :: Look.com skolem, thoralf (2) Sites. skolem Issue work. thoralf skolem (18871963)Biography from MacTutor History of mathematics archive. Helphttp://www.look.com/searchroute/directorysearch.asp?p=332678

 14. Directory :: Look.com Jan (2) Peirce, Charles Sanders (10) Post, Emil L. (5) Prior, Arthur Norman (2)Quine, Willard van Orman (9) Russell, Bertrand (17) skolem, thoralf (2) Tarskihttp://www.look.com/searchroute/directorysearch.asp?p=168896

 15. Logic - CASE Bibliography Universal Classes. In Baldwin, 19852, pp. 264-418. skolem, thoralf (1920). 252f.skolem, thoralf (1922). Some remarks on axiomatized set theory.http://david_hewins.tripod.com/papers/id13.html

16. Godel 3
1931. 1932d Review of thoralf skolem 1931, AMsS, 2 pp. 1932. 1932e 1932.1932n Review of thoralf skolem 1932, AMsS, 2 pp. 1932. 1933j
http://libweb.princeton.edu/libraries/firestone/rbsc/aids/godel/godel3.html
 IV. Drafts and Offprints Box/Folder AMs Notebook (in Gabelsberger shorthand) labelled "Diss. unrein," written both directions [1929?] TMs [carbon] (in German) labelled "Dissertation," with autograph corrections, 34 pp. [1929?] TMs (in German), labelled "Vollstandigkeit d. Axiome" with autograph corrections, 20 pp. [1930?] Printed page proof with autograph corrections [1930?] Offprint 1930 Galley with autograph annotations [1930] TMs (in German) with autograph corrections, pp. 10 [1930] AC describing contents of original file n.d. Erkenntnis 2 TMs [carbon] of discussion (in German) with autograph corrections, p. 23 ca.1930 TMs of Nachtrag ("Supplement"), with autograph corrections, 3 pp., back labelled "Erkenntnis" [1931?] TMs of Nachtrag with autograph corrections, p. 3 Offprint with autograph annotations [1931] Copy of Erkenntnis 2 with autograph annotations 1931 Undecidability Results (early drafts of AMs (in Gabelsberger shorthand) in 2 Notebooks, one inserted in the other, labelled "Unentsch. unrein," written both directions [1930?] AMs Notebook (in Gabelsberger shorthand), labelled "Unentsch. unrein," written both directions [1930?]

17. Logician's Year
Carnap Rudolf, (* 1891). 23 Mar, skolem, thoralf, (+ 1963). 24 Mar, Lorenzen,Paul, (* 1915). 21 May, Zermelo, Ernst, (+ 1951). 23 May, skolem, thoralf, (* 1887).June.
http://www.volny.cz/logici/vyroci/english.html
##### The Logician's Year
January February March April ... December
##### January
5 Jan Kleene, Stephen Cole 6 Jan Cantor, Georg 12 Jan Hintikka, Jaakko 14 Jan Carroll, Lewis Tarski, Alfred Gödel, Kurt 19 Jan Ramsey, Frank Plumpton 23 Jan Hilbert, David 26 Jan Kleene, Stephen Cole 27 Jan Carroll, Lewis
##### February
2 Feb Russell, Bertrand Artur William 3 Feb Lewis, Clarence Irving 6 Feb Arnauld, Antoine 8 Feb von Neumann, Johannes 11 Feb Post, Emil Leon 12 Feb Herbrand, Jean Dedekind, Richard 13 Feb £ukasiewicz, Jan 14 Feb Hilbert, David 15 Feb Whitehead, Alfred North 16 Feb Nicod, Jean 17 Feb Fraenkel, Adolf Abraham 22 Feb Ramsey, Frank Plumpton 27 Feb Brouwer, Luitzgen Egbertus Jan
##### March
3 Mar Cantor, Georg 5 Mar Barwise, Jon 6 Mar Davidson, Donald 7 Mar Montague, Richard 18 Mar de Morgan, Augustus Carnap Rudolf 23 Mar Skolem, Thoralf 24 Mar Lorenzen, Paul 25 Mar Ackermann, Wilhelm
##### April
2 Apr Vaught, Robert Lawson 4 Apr Venn, John Vaught, Robert Lawson 12 Apr Lewis, Clarence Irving 19 Apr Peirce, Charles Sanders 20 Apr Peano, Giuseppe 21 Apr Post, Emil Leon 26 Apr Wittgenstein, Ludwig 28 Apr Gödel, Kurt

18. Logikùv Rok
Translate this page Carnap Rudolf, (* 1891). 23. 3. skolem, thoralf, (+ 1963). 24. 23. 5. skolem,thoralf, (* 1887). Cerven. 7. 6. Turing, Alan Mathison, (+ 1954). 14.
http://www.volny.cz/logici/vyroci/
##### Logikùv rok
Leden Únor Bøezen Duben ... Prosinec
##### Leden
Kleene, Stephen Cole Cantor, Georg Hintikka, Jaakko Carroll, Lewis Tarski, Alfred Gödel, Kurt Ramsey, Frank Plumpton Hilbert, David Kleene, Stephen Cole Carroll, Lewis
##### Únor
Russell, Bertrand Artur William Lewis, Clarence Irving Arnauld, Antoine von Neumann, Johannes Post, Emil Leon Herbrand, Jean Dedekind, Richard £ukasiewicz, Jan Hilbert, David Whitehead, Alfred North Nicod, Jean Fraenkel, Adolf Abraham Ramsey, Frank Plumpton Brouwer, Luitzgen Egbertus Jan
##### Bøezen
Cantor, Georg Barwise, Jon Davidson, Donald Montague, Richard de Morgan, Augustus Carnap Rudolf Skolem, Thoralf Lorenzen, Paul Ackermann, Wilhelm
##### Duben
Vaught, Robert Lawson Venn, John Vaught, Robert Lawson Lewis, Clarence Irving Peirce, Charles Sanders Peano, Giuseppe Post, Emil Leon Wittgenstein, Ludwig Gödel, Kurt Wittgenstein, Ludwig
##### Kvìten
Löwenheim, Leopold Heyting, Arend Wang, Hao Russell, Bertrand Arthur William Wang, Hao Zermelo, Ernst Skolem, Thoralf
##### Èerven
Turing, Alan Mathison Church, Alonzo von Wright, Georg Henrik Turing, Alan Mathison Quine, Willard Van Orman

 19. Hippias: Limited Area Search Of Philosophy On The Internet Next Copyright notice Up thoralf Albert skolem 18871963 Previous thoralf Albertskolem 1887-1963 thoralf Albert skolem Professor thoralf Albert skolemhttp://hippias.evansville.edu/search.cgi?transfinite

 20. Hippias: Limited Area Search Of Philosophy On The Internet thoralf skolem and the Epsilon Substitution Method for Predicate Logic Next 1.Introduction Up Contents thoralf skolem and the Epsilon Substitution Methodhttp://hippias.evansville.edu/search.cgi?logic*&10

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