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  1. Abstract Set Theory by Thoralf Skolem, 1962-06
  2. Lattice Theorists: Thoralf Skolem, Garrett Birkhoff, Henry Wallman, Øystein Ore, Robert P. Dilworth, Alfred Horn, Bjarni Jónsson, Richard J. Wood
  3. Mathématicien Norvégien: Niels Henrik Abel, Sophus Lie, Atle Selberg, Thoralf Skolem, Ludwig Sylow, Kristen Nygaard, Axel Thue, Viggo Brun (French Edition)
  4. Albert Thoralf Skolem (German Edition)
  5. Primitive Recursive Arithmetic: Primitive Recursive Arithmetic, Quantification, Thoralf Skolem, Finitism, Foundations of Mathematics, Ordinal Analysis, Peano Axioms, Natural Number
  6. Primitive Recursive Function: Primitive Recursive Function, Primitive Recursive Arithmetic, Quantification, Thoralf Skolem, Finitism, Foundations of Mathematics, ... Analysis, Peano Axioms, Natural Number
  7. Primitive Recursive Arithmetic: Quantification, Thoralf Skolem, Finitism, Foundations of Mathematics, Ordinal Analysis, Peano Axioms, Natural Number, Primitive Recursive Function, Addition
  8. ABSTRACT SET THEORY. Notre Dame Mathematical Lectures Number 8. by Thoralf A. SKOLEM, 1962
  9. MODERN LOGIC: FROM FREGE TO GÖDEL: SKOLEM: An entry from Gale's <i>Encyclopedia of Philosophy</i> by Bede Rundle, 2006

1. Science, Math, Logic And Foundations, History, People: Skolem, Thoralf
Thoralf Skolem (18871963) - Biography from MacTutor History of mathematicsarchive. Help build the largest human-edited directory on the web.
http://www.combose.com/Science/Math/Logic_and_Foundations/History/People/Skolem,
Top Science Math Logic and Foundations ...
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2. Untitled
none Abstract Set Theory skolem thoralf Skolem 026800000X 1962 p $7.00 machines, Church's Thesis, compactness, LowenheimSkolem, Godel's Incompleteness theorems, Loeb's theorem
http://www.mathacademy.com/platonic_realms/books/books_list.txt

3. Thoralf Skolem
Thoralf Skolem. Albert Thoralf Skolem (May 23, 1887 March 23, 1963) was aNorwegian mathematician. He worked mostly on group theory. External link.
http://www.sciencedaily.com/encyclopedia/thoralf_skolem
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Thoralf Skolem
Albert Thoralf Skolem May 23 March 23 ) was a Norwegian mathematician. He worked mostly on group theory
External link
This article is a stub. You can help Wikipedia by expanding it. Note: The original source of this article can be found on the main Wikipedia Web site. This article is licensed under the GNU Free Documentation License , which means that you can copy and modify it as long as the entire work (including additions) remains under this license. About This Site Editorial Staff Contribute News Advertise With Us Science Daily editor@sciencedaily.com

4. Thoralf Skolem - Encyclopedia Article About Thoralf Skolem. Free Access, No Regi
encyclopedia article about Thoralf Skolem. Thoralf Skolem in Free onlineEnglish dictionary, thesaurus and encyclopedia. Thoralf Skolem.
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5. Skolem
Biography from MacTutor History of mathematics archive.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Skolem.html
Albert Thoralf Skolem
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 Other Web sites
  • Nordic Journal of Philosophical Logic
  • Mathematical Genealogy Project
    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
  • 6. Peter Suber, "The Löwenheim-Skolem Theorem"
    Suber, Philosophy Department, Earlham College. Review. skolem's Paradox. An Example of a NonStandard Model held interpretation is that of thoralf skolem himself. He believed that LST
    http://www.earlham.edu/~peters/courses/logsys/low-skol.htm
    Peter Suber Philosophy Department Earlham College Review members. A first-order theory is a system of predicate logic with a few additions. The motivation for the additions is to "outfit" the system to capture arithmetic. We may add denumerably many constants, so that it can name all the natural numbers. We may add countably many proper axioms (axioms which are not logically valid wffs) to supplement the logical axioms (axioms which are logically valid wffs) of predicate logic. If we take one 2-place predicate, say Pxy, and demand that all interpretations assign it the meaning of "identity" (so that Pxy means x=y), and if we add suitable proper axioms specifying the use of the new identity predicate, then we have a first-order theory with identity. The interpretations in which Pxy is given the stipulated meaning are called "normal" interpretations. First-order theories with identity have all the additions they need to capture arithmetic at least as well as well as arithmetic can be captured formally. While all first-order theories are vulnerable to LST, systems of arithmetic are the most important victims. Skolem's Paradox LST has bite because we believe that there are un countably many real numbers (more than ). Indeed, let's insist that we

    7. Skolem
    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
    Albert Thoralf Skolem
    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 Other Web sites
  • Nordic Journal of Philosophical Logic
  • Mathematical Genealogy Project
    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
  • 8. 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
    The URL of this page is:
    http://www-history.mcs.st-andrews.ac.uk/References/Skolem.html
  • 9. Considerations Regarding The Paradox Of Thoralf Skolem (1957) Paul
    22Considerations regarding the paradox ofthoralf skolem( 1957)Paul Bernays( Betrachtungen zum Paradoxon von thoralf skolem, 1957.)Translation by Dirk SchlimmComments Final revision
    http://www.phil.cmu.edu/bernays/Pdf/bernays22_2003-05-19.pdf

    10. 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.

    11. Thoralf Ulrick Qvale - ResearchIndex Document Query
    thoralf ulrick qvale scientific articles matching the query thoralf ulrick qvale Oxford University Press, 1991. Sko22 thoralf skolem. Einige Bemerkungen zur axiomatischen contribute substantially to finitist 4 thoralf skolem 1887-1963 History of constructivism
    http://citeseer.nj.nec.com/cs?q=Thoralf Ulrick Qvale

    12. Math: Logic And Foundations: History: People: Skolem, Thoralf
    Science Directory skolem, thoralf. archive. skolem, thoralf. Spacetransportation.org- Science Directory - Last Update Fri Apr 23 2004.
    http://www.spacetransportation.org/Math/Logic_and_Foundations/History/People/Sko
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    13. Math: Logic And Foundations: History: People
    4) Frege, Gottlob (11) G¶del, Kurt (8) Hilbert, David (6), Lukasiewicz, Jan(7) Peirce, Charles Sanders (11) Post, Emil L. (6) skolem, thoralf (2) Tarski
    http://www.spacetransportation.org/Math/Logic_and_Foundations/History/People/
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    14. 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
    Jens Erik Fenstad
    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.
    To make your own printed copy of this article, download one of the following files: Postscript: skobio.ps (186571 bytes)
    Postscript, compressed: skobio-ps.zip (45987 bytes)
    Adobe Acrobat: skobio.pdf (254065 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.

    15. Löwenheim-Skolem Notes
    The Löwenheimskolem Theorem is actually two theorems, both of which deal with the cardinality of In 1922, thoralf skolem presented a complete proof of this theorem (which
    http://www.cs.trinity.edu/~llanford/LS.html

    16. Science, Math, Logic And Foundations, History: People
    Russell, Bertrand@; skolem, thoralf; Tarski, Alfred; Turing, Alan Mathison;Wittgenstein, Ludwig@; Zermelo, Ernst. Related links of interest
    http://www.combose.com/Science/Math/Logic_and_Foundations/History/People/
    Top Science Math Logic and Foundations ... Zermelo, Ernst Related links of interest: SItes about logicians of historic importance. Help build the largest human-edited directory on the web. Submit a Site Open Directory Project Become an Editor The combose.com directory is based on the Open Directory and has been modified and enhanced using our own technology. About ComboSE Download Combose Toolbar

    17. :: Ez2Find :: Skolem, Thoralf
    Guide skolem, thoralf, Guides, skolem, thoralf. ez2Find Home Directory Science Math Logic and Foundations History People skolem, thoralf (2)
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    18. NJPL Volume 1, Number 2
    JENS ERIK FENSTAD. thoralf ALBERT skolem 18871963 HERMAN RUGE JERVELL. thoralf skolem PIONEER OF COMPUTATIONAL LOGIC
    http://www.hf.uio.no/filosofi/njpl/vol1no2
    VOLUME 1 NUMBER 2 DECEMBER 1996
    J ENS E RIK F ENSTAD
    THORALF ALBERT SKOLEM 18871963:

    A BIOGRAPHICAL SKETCH
    H ERMAN R UGE J ERVELL
    THORALF SKOLEM: PIONEER OF COMPUTATIONAL LOGIC

    THE SKOLEM LECTURES AT THE UNIVERSITY OF OSLO
    H AO W ANG
    SKOLEM AND GÖDEL
    G RIGORI M INTS
    THORALF SKOLEM AND THE EPSILON SUBSTITUTION

    METHOD FOR PREDICATE LOGIC

    M ATTI E KLUND
    ON HOW LOGIC BECAME FIRST-ORDER
    J AAKKO H INTIKKA AND G ABRIEL S ANDU
    A REVOLUTION IN LOGIC?
    SCANDINAVIAN UNIVERSITY PRESS Oslo - Copenhagen - Stockholm - Boston Last modified: Wed Mar 5 22:52:27 1997

    19. :: Ez2Find :: People
    Jan (7) Peirce, Charles Sanders (11) Post, Emil L. (6) Prior, Arthur Norman (2),Quine, Willard van Orman (12) Russell, Bertrand (21) skolem, thoralf (2) Tarski
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    20. Steps Towards A Logic Of Natural Objects
    wellfoundedness and Foundation Mirimanoff 1917, skolem 1922), but its separate status was Cambridge University Press, 1962. skolem, thoralf (1922). Some remarks on axiomatized set
    http://www.math.baruch.cuny.edu/~lkirby/naturalobjects.html
    Back to Laurence Kirby's home page Steps towards a logic of natural objects Laurence Kirby Baruch College, City University of New York
    This article appeared in Epistemologia vol XXV (2002), pp.225-244. 1. Introduction
    The natural objects that I propose to consider are broadly those physical objects which are studied and referred to by science and by a common sense view, informed by science, of the world. Natural objects are, philosophically speaking, individuals ; they are involved as units in dynamic, causal processes. I shall draw a distinction between natural objects and the abstract objects of mathematics, in particular set theory. Natural objects encompass atoms and molecules; cells and organisms, including you and me; the objects of everyday life such as chairs and automobiles; nations, continents, ecosystems, mountain ranges, geological faults; planets, stars and galaxies. Each natural object, when regarded internally, is a dynamic system with various interacting parts and components (some of which may be natural objects in their own right); when regarded externally, a natural object acts as a unit with respect to a larger system or systems (which may again be natural objects) of which the given object forms a part or component. It is sometimes argued that objects such as atoms or galaxies are theoretical constructs, as much so as mathematical objects (or even, according to some, more so). It is true that any reference to an object rests on epistemological assumptions. The approach here will be not to belittle these important epistemological questions but to leave them aside, and accept as a working assumption the practical viewpoint of people who are dealing with the world: that natural objects exist, act, and are acted upon, independently of the observer although any description of them or of their actions is dependent on the describer.

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