61. From Ralph Freese (ralph@math.hawaii.edu) July 1 Not Long Ago (ususually just called the word problem) had be solved in 1920 by thoralf skolem . Here is another relevant reference, which extends skolem s result. http://ttic.uchicago.edu/~dmcallester/lics-tutorial-feedback.txt

July 8 David, Thanks for your message and the references. Here is another relevant reference, which extends Skolem's result. Best, Phokion - >From MELVYL@UCCMVSA.UCOP.EDU Tue Jul 8 09:42:18 1997 Return-Path: Received: from uccmvsa.ucop.edu (uccmvsa.ucop.edu [128.48.140.3]) by lorraine.loria.fr (8.8.5/8.8.5/8.8.5/JCG) with SMTP id JAA18168 for ; Tue, 8 Jul 1997 09:42:15 +0200 (MET DST) Message-Id: Received: from UCCMVSA.UCOP.EDU by uccmvsa.ucop.edu (IBM MVS SMTP V3R1) with BSMTP id 7871; Tue, 08 Jul 97 00:42:15 PDT Received: by UCCMVSA.UCOP.EDU Tue, 08 Jul 97 00:42:07 PDT Date: Tue, 08 Jul 97 00:42:07 PDT From: Melvyl System

62. DMG-FG2: Projects skolem functions can be traced back to the famous paper by thoralf skolem 1920.Model theoretically they allow for the representation of abstract http://www.dmg.tuwien.ac.at/fg2/index.php?id=38

63. [math/0506155] Perfect Skolem Sets A set A that can be used to construct skolem sequences is called a skolem set . are skolem sets was solved by thoralf skolem in the late 1950 s. http://arxiv.org/abs/math.CO/0506155

Mathematics, abstract math.CO/0506155 From: Gustav Nordh [ view email ] Date: Wed, 8 Jun 2005 21:31:39 GMT (44kb) Perfect Skolem sets Authors: Gustav Nordh Subj-class: Combinatorics MSC-class: Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv math find abs

64. Greg Restall * Great Moments In Logic... Image of skolem thoralf skolem was a Norwegian logician and mathematician whocontinued the development of set theory along the lines started by Cantor http://consequently.org/archive/2001/11/

@import "2004.css"; consequently.org/writing/logicians Search this site home writing news archive zachary ... AJL Post a comment Name: Email Address: URL: Remember personal info? Yes No Comments: Great Moments in Logic Bernhard Bolzano (1781-1848) best known for what he has done in mathematics : the precise definition of continuity when it comes to real-valued functions. But for my money (and in my discipline) Bolzano was worth much more than this. He was the first philosopher to give a precise analysis of logical consequence in terms we would recognise today. (This was important for his project of understanding mathematics, and making it clearer, because mathematicians were getting into knots considering infinite numbers, infinitesimal Anyway, he argued that you can tell that an argument from premises to a conclusion is logically valid if and only if it never proceeds from truth to falsity no matter how you change the non-logical vocabulary in the argument. So Sally is coming to the party. If Sally is coming to the party, Jim will be happy. Therefore Jim will be happy.

65. Beezer's Academic Genealogy It seems odd that TCSG lists Ore as a student of skolem, with Ore s degree awarded Albert thoralf skolem TCSGMHMBDM; Axel Thue TCSGMHM BDM http://buzzard.ups.edu/genealogy.html

Beezer's Academic Genealogy Here it is the succession of PhD advisers and students that goes backwards in time from my own degree. For the later entries it is not clear that there was a formal advisor/student/degree relationship, but there is evidence that one person was influenced in their education by the other. It seems odd that [TCSG] lists Ore as a student of Skolem, with Ore's degree awarded in 1924 while [BDM] lists Skolem's degree as being given in 1926. Tree Paul Morris Weichsel (Cal Tech 1960) [ MGP Richard Albert Dean (Ohio State 1953) [ MGP Marshall Hall, Jr. (Yale University 1936) [ MGP TCSG MGP TCSG Albert Thoralf Skolem [ TCSG MHM ][BDM] Axel Thue [ TCSG MHM ] [BDM] Marius Sophus Lie [ MHM Peter Ludwig Mejdell Sylow [ MHM The following quotes are from articles in the Biographical Dictionary of Mathematicians [BDM]: Skolem: "In the latter year [1916] he returned to Oslo, where he was made Dozent in 1918. He received his doctorate in 1926." (H. Oettel, p. 2296) Thue: "Thue enrolled at Oslo University in 1883 and became a candidate for the doctorate in 1889." (Viggo Brun, p. 2460)

66. Bibliography skolem, thoralf Albert, 18871963, Selected works in logic, by Th. skolem / editedby Jens Erik Fenstad, Oslo, Universitetsforlaget, 1970 http://www.library.cornell.edu/math/bibliography/display.cgi?start=S&

67. Encyclopedia: Löwenheim-Skolem Theorem The theorem is named for Leopold Löwenheim and Albert thoralf skolem (May 23,1887 March 23, 1963) was a Norwegian mathematician. http://www.nationmaster.com/encyclopedia/Löwenheim_Skolem-theorem

Supporter Benefits Signup Login Sources ... Pies What's new? Our next offering Latest newsletter Student area Lesson plans Recent Updates Abisko A.S. Livorno Calcio 5 (number) 36446 Cinodapistoia ... More Recent Articles Top Graphs Richest Most Murderous Most Taxed Most Populous ... More Stats Encyclopedia: L¶wenheim-Skolem theorem Updated 135 days 13 hours 17 minutes ago. Other descriptions of L¶wenheim-Skolem theorem In Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. Although the layperson may think that mathematical logic is the logic of mathematics, the truth is rather that it more... mathematical logic , the classic Skolem theorem states that any infinite "model" M has a countably infinite submodel N that satisfies exactly the same set of First-order predicate calculus or first-order logic (FOL) is a theory in symbolic logic that permits the formulation of quantified statements such as there is at least one X such that... or for any X, it is the case that..., where X is an element of a set called... first-order sentences that M satisfies. A "model", in this sense, consists of an underlying set (often also denoted) "

68. Encyclopedia: Thoralf Skolem More results from www.nationmaster.com INDEX OF NAMESSkolem, A. thoralf (Norway, 18871963) and non-standard arithmetic, 1169 and settheory, 1154 Smale, Stephen (USA, 1930- ) and chaos theory, 971 http://www.nationmaster.com/encyclopedia/Thoralf-Skolem

Supporter Benefits Signup Login Sources ... Pies Related Articles People who viewed "Thoralf Skolem" also viewed: Skolemization Spencer family George H. W. Bush What's new? Our next offering Latest newsletter Student area Lesson plans Recent Updates Abisko A.S. Livorno Calcio 5 (number) 36446 Cinodapistoia ... More Recent Articles Top Graphs Richest Most Murderous Most Taxed Most Populous ... More Stats Encyclopedia: Thoralf Skolem Updated 205 days 2 hours 25 minutes ago. Other descriptions of Thoralf Skolem Albert Thoralf Skolem May 23 March 23 ) was a Norwegian mathematician. He worked mostly on mathematical logic See: Löwenheim-Skolem theorem Skolemization Skolem function Skolem normal form ... Skolem-Noether theorem External link Short biography http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Skolem.html Categories Stub 1887 births 1963 deaths ... Norwegian scientists Click for other authoritative sources for this topic (summarised at Factbites.com) The Wikipedia article included on this page is licensed under the GFDL Usage implies agreement with terms

69. Historia Matematica Mailing List Archive: [HM] Mathematical Induction above, because thoralf skolem (another giant) was the first who saw clearly thehuge difference between the principle of mathematical http://sunsite.utk.edu/math_archives/.http/hypermail/historia/mar99/0101.html

[HM] mathematical induction Carlos Cesar de Araujo lavarini@digitus.com.br 21 Mar 99 16:28:04 -0500 (EST) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: John Conway: "Re: [HM] Euclid, Book II" Previous message: Ken Pledger: "Re: [HM] Euclid, Book II" This note is a hasty attempt to answer the question about the first to formalize mathematical induction. "Mathematical induction" has a fascinating history really. I am still waiting for a complete discussion of it, one which would include not only the names of Euclid, al-Karaji, Levi ben Gerson, Maurolycus, Pascal, Fermat, Wallis, Jacob Bernoulli, De Morgan, Grassmann, Frege, Dedekind, Peano, Poincare' and Russell, but of Padoa, Pieri, Hilbert, Skolem, von Neumann, Landau, Henkin, Shepherdson and Moschovakis as well. Despite all these names, Richard Dedekind was the first man who formalized the principle in a clear, elegant, rigorous and "modern" set-theoretical fashion. This he did in his Was sind und Was sollen die Zahlen? [VI, Definition 71], first published in 1887 after "a first rough draft which several mathematicians examined" and which was prepared "in the years 1872 to 1878". He understood completely, more

70. Thoralf Skolem Université Montpellier II Translate this page thoralf skolem (1887-1963). Cette image et la biographie complète en anglaisrésident sur le site de l’université de St Andrews Écosse http://ens.math.univ-montp2.fr/SPIP/article.php3?id_article=1820

71. Directorio - Enlaces Russell,_Bertrand@ (18); skolem, thoralf (2); Tarski, Alfred (5) Quine,Willard van Orman @ (12); Russell, Bertrand @ (18); skolem, thoralf (2) http://www.satd.uma.es/matap/svera/links/matnet1.html

Análisis Matemático Asociaciones Constantes Pi Análisis Matemático Asociaciones Constantes Pi ... Knot Theory

72. Famous Computer Scientists skolem constant thoralf skolem (18871963). A skolem constant is a new constantthat is substituted for a variable when eliminating an existential http://www.comp.leeds.ac.uk/roger/Famous/eponymy_content.html

Abigailisms abigail@delanet.com. An Abigailism is a response to a question containing basic cognitive errors posed to a newsgroup (in particular, comp.lang.perl.misc ). An example: Q. Do I need to test Perl scripts on a web server or can it be done offline? A. Do I need to have a bell on my bicycle, or can I ride it wearing a hat? Ada Ada Byron, Lady Lovelace (1815-1852). The Ada language was named after her. She was an assistant of Babbage, and arguably the first ever computer programmer. Web material on her abounds. Armstrong's Axioms William W. Armstrong. Armstrong's Axioms are rules of inference for functional dependencies. AWK Alfred Aho, Peter Weinberger, Brian Kernighan. A Unix-based text/handling/macro programming language. Backus-Naur form John Backus, Peter Naur A formal metasyntax used to express context-free grammars. Bernoulli drive Daniel Bernoulli (1700-1782). Just like a disk drive but faster and more rugged - however not as fast as a hard drive. Bernstein's Conditions Arthur Bernstein.

73. [FOM] Order Type Of Non-standard Models I went to the library last week and got hold of thoralf skolem s Selected Worksin Logic , edited by Fenstad. My memory of the reference to order types of http://www.cs.nyu.edu/pipermail/fom/2003-August/007132.html

[FOM] Order type of non-standard models Alasdair Urquhart urquhart at cs.toronto.edu Mon Aug 4 13:07:58 EDT 2003 Previous message: [FOM] Structure of nonstandard models of PA Next message: [FOM] math foundations webpage Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Previous message: [FOM] Structure of nonstandard models of PA Next message: [FOM] math foundations webpage Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

74. FOM: Non-standard Models Hao Wang on p.41 of A survey of skolem s work in logic thoralf skolem SelectedWorks in Logic, ed.JEFenstad, Oslo 1970, pp.1752 comments that passage http://www.cs.nyu.edu/pipermail/fom/1997-December/000382.html

FOM: non-standard models Walter Felscher walter.felscher at uni-tuebingen.de Tue Dec 2 09:28:35 EST 1997 Previous message: FOM: Peter Simons' essay on Frege's theory of real numbers Next message: FOM: Feferman on inherent vagueness of CH Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] I would like to know the earliest documented observation that there are non-standard models for the theory of arithmetic. I am interested not so much in date of first publication, as date of first realization of this fact. Previous message: FOM: Peter Simons' essay on Frege's theory of real numbers Next message: FOM: Feferman on inherent vagueness of CH Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

75. Golem.de - Lexikon Translate this page Dieser Artikel basiert auf dem Artikel Albert thoralf skolem aus der freienEnzyklopädie Wikipedia und steht unter der GNU Lizenz für freie Dokumentation. http://lexikon.golem.de/Albert_Thoralf_Skolem

News Forum Archiv Markt ... Impressum Lexikon-Suche Lizenz Dieser Artikel basiert auf dem Artikel Albert Thoralf Skolem aus der freien Enzyklopädie Wikipedia und steht unter der GNU Lizenz für freie Dokumentation . In der Wikipedia ist eine Liste der Autoren verfügbar, dort kann man den Artikel bearbeiten Letzte Meldungen IFA: Veranstalter und Aussteller hochzufrieden Sanyo-Projektor PLV-Z4: Leise und kontraststark ... Originalartikel Lexikon: Albert Thoralf Skolem Albert Thoralf Skolem 23. Mai in Sandsvaer in Oslo ) war ein norwegischer Mathematiker, Logiker und Philosoph. Seine Arbeiten lieferten grundlegende Resultate zur mathematischen Logik Mittels der nach ihm benannten Normalform Skolemform genannt wird. Skolem wies auch auf die scheinbar paradoxen Konsequenzen dieses Satzes hin (" Skolem-Paradox Durch Skolem wurde in der Axiomatisierung der Mengenlehre der Schlusspunkt gesetzt, indem er mit den Mitteln der Formalisierung dem Komprehensionsaxiom primitiv-rekursiven Funktion Peano-Aritmetik Entscheidungsproblem Werke Some remarks on recursive arithmetic Bemerkungen zum Komprehensionsaxiom Personendaten NAME Skolem, Albert Thoralf

76. BIOGRAPHIES OF PAST NUMBER THEORISTS And VARIOUS ITEMS OF HISTORICAL INTEREST Albert thoralf skolem (MacTutor); thoralf Albert skolem (A Biographical SketchJens Erik Fenstad, Nordic Journal of Philosophical Logic, Vol. 1, No. http://www.numbertheory.org/ntw/N14.html

Biographies of past number theorists and various items of historical interest Cornell Digital Library Math Collection : Old Mathematics books listed by Title - including Hensel, Sommer Mathematicians of the Seventeenth and Eighteenth Centuries , Hasse's work on the Riemann hypothesis for curves over finite fields - An historical perspective by Professor Peter Roquette (plus notes on class-field theory, Artin L-functions, Erich Hecke) Two Hundred Years of Number Theory after Carl-Friedrich Gauss's Disquisitiones Arithmeticae , A list of lectures at an Oberwolfach conference, June 17-23, 2001 Aus der Geschichte der Zahlentheorie (Wolfgang Schwarz - pdf) Collected Works Collected papers of Peter Roquette , editors: Anthony V. Geramita and Paulo Ribenboim, Queens University Ouvres J.-P. Serre I-III , Springer 2003 , AMS Notices, March 2005 On the AMS Notices Publication of Krieger's Translation of Weil's 1940 Letter , by Serge Lang, AMS Notices, July 2005 Biographies The Man Who Knew Infinity (A life of the genius Ramanujan), R. Kanigel, Washington Square Press 1992 The Apprenticeship of a Mathematician The mountains of Pi , an article about Gregory and David Chudnovsky, by Richard Preston The Life of Alexandre Grothendieck , part (a), AMS Notices October 2004 The Life of Alexandre Grothendieck , part (b), AMS Notices November 2004 Prizes John Tate awarded a Wolf Prize for 2003 SASTRA Ramanujan Prize Serre receives Abel prize , Notices of the AMS, Volume 50, Number 6, 2003 Serre awarded Abel Prize Interview with Jean-Pierre Serre , NAMS February 2004

77. Matematisk Vekst I Abels Fotspor Også Axel Thue, thoralf skolem, Viggo Brun, Ernst Selmer, thoralf skolempubliserte hele 177 avhandlinger i løpet av sin lange karriere. http://www.forskning.no/Artikler/2002/juni/1023116423.71/artikkel_print

Matematisk vekst i Abels fotspor 04.jun 2002 07:00 Av: Bjarne Røsjø , Informasjonsrådgiver Niels Henrik Abel er ett av de største matematiske genier verden har fostret, og årets 200-årsjubileum brukes til å markere hans innsats. Det er ikke fullt så godt kjent at det grodde friskt i sporene etter Abel så godt at Norge nærmest var en matematisk stormakt på slutten av 1800-tallet og langt utover på 1900-tallet. - Du skal ikke åpne mange lærebøker i avansert matematikk før du støter på Axel Thues teorem, Sophus Lies grupper eller Ludwig Sylows teorier. Norge som nasjon var overrepresentert med fremragende matematikere på slutten av 1800-tallet, forteller Geir Ellingsrud, som er professor i matematikk ved UiO og deltaker i årets forskningsgruppe i matematikk ved SHS. – Også Axel Thue, Thoralf Skolem, Viggo Brun, Ernst Selmer, Vilhelm Ljunggren og ikke minst Selberg har gitt viktige bidrag til tallteoriens gullalder, forteller Ellingsrud. En systematisk oppbygging Professor Jens Erik Fenstad ved Matematisk institutt ved UiO er enig i at Norge har fostret uvanlig mange fremragende matematikere.

78. Albert Thoralf Skolem - Wikipedia Translate this page Literatur von und über Albert thoralf skolem im Katalog der DDB. Personendaten.NAME, skolem, Albert thoralf. ALTERNATIVNAMEN http://de.wikipedia.org/wiki/Albert_Thoralf_Skolem

Es ist geschafft - unser Spendenziel von 200.000$ ist erreicht . Herzlichen Dank an alle Spender. Albert Thoralf Skolem aus Wikipedia, der freien Enzyklop¤die Albert Thoralf Skolem 23. Mai in Sandsvaer 23. M¤rz in Oslo ) war ein norwegischer Mathematiker, Logiker und Philosoph. Seine Arbeiten lieferten grundlegende Resultate zur mathematischen Logik , insbesondere zu den Bereichen Modelltheorie und Berechenbarkeit. Aber auch zur mathematischen Grundlagenforschung wie Pr¤dikatenlogik, Klassenlogik, Rekursionstheorie, Mengenlehre und Grundlagen der Arithmetik leistete er wesentliche Beitr¤ge. Mittels der nach ihm benannten pr¤dikatenlogischen Normalform Skolemform ) hat er f¼r den Satz von L¶wenheim , daŸ jeder erf¼llbare Ausdruck des Pr¤dikatenkalk¼ls schon in einem h¶chstens abz¤hlbaren Bereich erf¼llbar ist, einen ¼berschaubaren Beweis gegeben, so daŸ dieser Satz heute mit Recht Satz von L¶wenheim und Skolem genannt wird. Skolem wies auch auf die scheinbar paradoxen Konsequenzen dieses Satzes hin (" Skolem-Paradox Durch Skolem wurde in der Axiomatisierung der Mengenlehre der Schlusspunkt gesetzt, indem er mit den Mitteln der Formalisierung dem

79. Descendants Of Morten Anundsøn Strenge skolem, thoralf Albert (18711886)C. skolem, thoralf Albert (1887- )C. skolem,Thorbjørn Tøgersen (1889-1940)P,P. skolem, Timand Torkelsen (1810-1898)P http://home.no.net/arnehol/genealogy/Lintvedt/Names33.htm

My Lintvedt family, descendants of Morten Anundsøn Strenge A B C D ... P , Q, R S T U ... W , X, Y, Z About this family Names Saatvedt, Anna (1929- ) C Saatvedt, Astrid (1920- ) C Saatvedt, Berit (1959- ) C Saatvedt, Gjertrud Irene (1934- ) P Saatvedt, Haldis Kristine Grosvold (1923- ) P Saatvedt, Ingrid (1927- ) C Saatvedt, Ivar Ole ( - ) S Saatvedt, Kjell (1963- ) C Saatvedt, Knut Wilhelm Omholt (2001- ) C Saatvedt, Kristian Olausen (1926- ) C Saatvedt, Magne Vincent (1934- ) C Saatvedt, Olav (1932-1935) C Saatvedt, Ole Kristian (1997- ) C Saatvedt, Ole Lukassøn (1764-1848) S Sabel, Ingrid Marie ( - ) C Sabel, James Robert (1956- ) C Sabel, John Gordon ( - ) C Sabel, Karen Louise ( - ) C Sabel, Kristin Elaine (1962- ) C Sabel, Paul Frederick ( - ) C Sabel, Robert Walter ( - ) S Sæther, Arne ( - ) S Sæthre, Anne ( -1949) S Sæthre, Signy ( - ) P Sætra, Anne Grethe (1965- ) S Sætra, Asbjørn Ludvig (1938- ) P Sætra, Erik Torbjørn (1943- )

80. Albert Thoralf Skolem - Wikipedia Albert thoralf skolem Albert thoralf skolem, norveški matematik, logik infilozof, skolem je študiral matematiko na Univerzi v Kristianiji. http://sl.wikipedia.org/wiki/Albert_Thoralf_Skolem

Wikimedija potrebuje vaÅ¡o pomoč pri zbiranju 200.000 dolarjev . Za podrobnosti glejte stran o zbiranju prispevkov Od 19. avgusta smo zbrali že preko 185.000$. Hvala za vaÅ¡o velikoduÅ¡nost! Albert Thoralf Skolem Iz Wikipedije, proste enciklopedije. Albert Thoralf Skolem norveÅ¡ki matematik logik in filozof 23. maj Sandsvaer Buskerud ... Oslo Skolem je Å¡tudiral matematiko na Univerzi v Kristianiji . Leta je doktoriral . Od leta je bil asistent fiziku Kristianu Birkelandu Največ se je ukvarjal z matematično logiko . Leta je dokazal, da za naravna Å¡tevila ne moremo najti sistema značilnih lastnosti aksiomov . Dokazoval je tudi, da obstaja množica reči, ki ustreza Peanovim aksiomom in ni izomorfna množici naravnih Å¡tevil spremeni Dela Diophantische Gleichungen (Springer, Berlin Sur la porte© de L¶wenheim-Skolem Einige Bemerkungen ¼ber die Induktionsschemata in der rekursiven Zahlentheorie Some remarks on recursive arithmetic Bemerkungen zum Komprehensionsaxiom spremeni Glej tudi L¶wenheim-Skolemov izrek skolemizacija Skolemova funkcija Skolemova normalna oblika ... spremeni Zunanje povezave Stran o Albertu Thoralfu Skolemu Univerze St Andrews (v angleščini biografski članek je Å¡krbina . Slovenski Wikipediji lahko pomagate tako, da ga dopolnite z vsebino.

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