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Skolem Thoralf:     more detail

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

lists with details

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,

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

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.  
   http://encyclopedia.thefreedictionary.com/Thoralf Skolem

5. Skolem
   Biography from MacTutor History of mathematics archive.  
   http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Skolem.html
   
   Extractions: 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.

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
   
   Extractions: 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
   
   Extractions: 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.

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
   
   Extractions: 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

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

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

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/

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

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/
    
    Extractions: 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)  
    http://ez2find.com/cgi-bin/directory/meta/search.pl/Science/Math/Logic_and_Found
    
    Extractions: Any Language English Afrikaans Arabic Bahasa Melayu Belarusian Bulgarian Catala Chinese Simplified Chinese Traditional Cymraeg Czech Dansk Deutsch Eesti Espanol Euskara Faroese Francais Frysk Galego Greek Hebrew Hrvatski Indonesia Islenska Italiano Japanese Korean Latvian Lietuviu Lingua Latina Magyar Netherlands Norsk Polska Portugues Romana Russian Shqip Slovensko Slovensky Srpski Suomi Svenska Thai Turkce Ukrainian Vietnamese Mode Guides Skolem, Thoralf Web Sites Skolem Issue of the Nordic Journal of Philosophical Logic [Site Info] [Translate] [Open New Window] Thoralf Skolem (1887-1963) [Site Info] [Translate] [Open New Window] Biography from MacTutor History of mathematics archive. URL: http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Skolem.html

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

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  
    http://ez2find.com/cgi-bin/directory/meta/search.pl/Science/Math/Logic_and_Found
    
    Extractions: Any Language English Afrikaans Arabic Bahasa Melayu Belarusian Bulgarian Catala Chinese Simplified Chinese Traditional Cymraeg Czech Dansk Deutsch Eesti Espanol Euskara Faroese Francais Frysk Galego Greek Hebrew Hrvatski Indonesia Islenska Italiano Japanese Korean Latvian Lietuviu Lingua Latina Magyar Netherlands Norsk Polska Portugues Romana Russian Shqip Slovensko Slovensky Srpski Suomi Svenska Thai Turkce Ukrainian Vietnamese Mode Choose State/Prov. Alabama Alaska Alberta Arizona Arkansas British Columbia California Colorado Connecticut D.C. Delaware Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Manitoba Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Brunswick New Hampshire New Jersey New Mexico New York Newfoundland North Carolina North Dakota Northwest Terr. Nova Scotia Ohio Oklahoma Ontario Oregon Pennsylvania Prince Edward Isl.

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
    
    Extractions: 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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