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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

41. Skolem Arrays
    skolem arrays are an extension of skolem sequences which were studied inthe 1950s by the Norwegian mathematician thoralf skolem(18871963).  
    http://mathcs.mta.ca/research/cbaker/skolem/
    
    Extractions: Skolem arrays are an extension of Skolem sequences which were studied in the 1950s by the Norwegian mathematician Thoralf Skolem(1887-1963). A Skolem sequence of order n is a sequence of integers which satisfies the following properties: The two occurrences of i are exactly i integers apart. The sequence

42. The Results Of Our Project
    The Results of Our Project. thoralf skolem proved that n = 0,1 mod 4 was anecessary and sufficient condition for the existence of skolem sequences.  
    http://mathcs.mta.ca/research/cbaker/skolem/results.htm
    
    Extractions: Thoralf Skolem proved that n 0,1 mod 4 was a necessary and sufficient condition for the existence of Skolem sequences. Similarly, we have proven that n 0,1 mod 4 is also a necessary and sufficient condition for the existence of Skolem arrays. Despite this, we have yet to find a direct link between Skolem sequences and Skolem arrays. Current research is devoted to finding a link between Skolem arrays and combinatorial designs. A split pair occurs when the two instances of a number appear on different rows. We conjecture that in all Skolem arrays, the number of split pairs is greater than or equal to the number of unsplit pairs.

43. Who Are Boole, Fitch, And Tarski?
    skolem, thoralf (18871963) Norwegian logician known especially for the Löwenheim-skolem Theorem and skolem s Paradox It follows from the Löwenheim-skolem  
    http://www.ucalgary.ca/~rzach/279/logicians.html

44. Bibliography
    Kazan. Univ. 1966. skolem, thoralf Albert, 18871963, Selected works in logic,by Th. skolem / edited by Jens Erik Fenstad, Oslo, Universitetsforlaget, 1970.  
    http://www.library.cornell.edu/math/bibliography/display.cgi?start=S&

45. Forskning.no: Matematisk Vekst I Abels Fotspor
    Også Axel Thue, thoralf skolem, Viggo Brun, Ernst Selmer, Vilhelm thoralfskolem publiserte hele 177 avhandlinger i løpet av sin lange karriere.  
    http://www.forskning.no/Artikler/2002/juni/1023116423.71
    
    Extractions: 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.

46. Open Directory - Science: Math: Logic And Foundations: History: People: Skolem,
    Mints, Matti Eklund on skolem s life and work. thoralf skolem (18871963)- Biography from MacTutor History of mathematics archive.  
    http://www.newhoo.com/Science/Math/Logic_and_Foundations/History/People/Skolem,_

47. Descendants Of Morten Anundsøn Strenge
    skolem, Svein (1879 ) C. skolem, thoralf Albert (1871-1886) C. skolem,thoralf Albert (1887- ) C. skolem, Thorbjørn Tøgersen (1889-1940) P,P.  
    http://home.no.net/arnehol/genealogy/Lintvedt/Names33.htm
    
    Extractions: 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 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- )

48. My Johnson Family, Descendants Of Morten Anundsøn Strenge
    2286 M i. thoralf Albert skolem was born on 15 May 1871 and died on 6 Jan 1886, atage 14. 2287 M ii. 2291 M vi. thoralf Albert skolem was born on 23 May 1887.  
    http://home.no.net/arnehol/genealogy/Lintvedt/D9.htm
    
    Extractions: 1208. Helle Syrene Paulsdatter Røsholt Paul Andersøn Røsholt , Anders Pålsøn Røsholt , Berte Marie Hansdatter Hvål , Sigrid Anundsdatter Søum , Anund Mortensøn , Morten Anundsøn , Anund Mortensøn , Morten Anundsøn ) was born in 1843 in Røsholt, Sandsvær, Bu. and died in 1879, at age 36.

49. The Mathematics Genealogy Project - Index Of SK
    Skokan, Jozef, Emory University, 2000. skolem, thoralf, Universiteteti Oslo, 1926. Skoogh, Daniel, Chalmers University of Technology, 1998.  
    http://genealogy.impa.br/html/letter.phtml?letter=SK

50. Wiki: SkolemFunction
    finite model. In 1922, thoralf skolem presented a complete proof ofthis theorem (which is now called the Löwenheimskolem Theorem).  
    http://gnufans.net/intrspctr.pl?SkolemFunction

51. Model Theory. Goedel's Completeness Theorem. Skolem's Paradox. Ramsey's Theorem.
    Initially, Model Existence theorem was proved in a weaker form in 1915 (by LeopoldLoewenheim) and 1919 (by thoralf skolem) if a first order theory has a model  
    http://www.ltn.lv/~podnieks/gta.html
    
    Extractions: model theory, Skolem paradox, Ramsey theorem, Loewenheim, categorical, Ramsey, Skolem, Gödel, completeness theorem, categoricity, Goedel, theorem, completeness, Godel Back to title page Left Adjust your browser window Right Some widespread Platonist superstitions were derived from other important results of mathematical logic (omitted in the main text of this book): Goedel's completeness theorem for predicate calculus, Loewenheim-Skolem theorem, the categoricity theorem of second order Peano axioms. In this short Appendix I will discuss these results and their methodological consequences (or lack of them). All these results have been obtained by means of the so-called model theory . This is a very specific approach to investigation of formal theories as mathematical objects. Model theory is using the full power of set theory. Its results and proofs can be formalized in the set theory ZFC Model theory is investigation of formal theories in the metatheory ZFC. The main structures of model theory are interpretations . Let L be the language of some (first order) formal theory containing constant letters c , ..., c

52. Resolution Method. Normal Forms. Skolem. Mathematical Logic. Part 5.
    The second step (idea 2b, due to thoralf skolem) allows elimination of existentialquantifiers. It was first introduced by thoralf skolem (18871963) in 1928  
    http://www.ltn.lv/~podnieks/mlog/ml5.htm
    
    Extractions: normal form, prenex, disjunctive, conjunctive, form, normal, DNF, CNF, prenex normal form, Skolem normal form, disjunctive normal form, conjunctive normal form, Skolem Back to title page Left Adjust your browser window Right Prenex normal form Conjunctive and disjunctive normal forms Skolem normal form Clause form ... Resolution method for predicate formulas In this section, we will try to produce a practical method allowing to prove theorems by using computers. In general, this task is not feasible because of its enormous computational complexity (see Section 6 ). Still, for problems of a "practical size" (arising, for example, in deductive databases and other artificial intelligence systems, or, trying to formalize real mathematical proofs), such methods are possible and some of them are already successfully implemented. Mizar project QED project Classical logic only... Main Ideas If F , ..., F n is the set of our assumptions (facts, rules, axioms, hypotheses etc.), does the assertion G follow from this set? One of the well known approaches to proving theorems in mathematics are the so-called refutation proofs (reductio ad absurdum) - proofs by deriving a contradiction: assume ~G, and derive a contradiction. I.e. prove that F

53. SearchBug Directory: Science: Math: Logic_and_Foundations: History: People
    Jan (7) Peirce, Charles Sanders (11) Post, Emil L. (6) Prior, Arthur Norman (2),Quine, Willard van Orman (12) Russell, Bertrand (23) skolem, thoralf (2) Tarski  
    http://www.searchbug.com/directory.aspx/Science/Math/Logic_and_Foundations/Histo

54. The Norwegian Mathematical Society.
    Matematisk Tidsskrift ( The Norwegian Mathematical Journal ) appeared in 1919,opening, sadly, with the obituary of Ludvig Sylow, written by thoralf skolem.  
    http://www.matematikkforeningen.no/enghist.html
    
    Extractions: by Bent Birkeland [The summary of the society's history below is not a direct translation of the Norwegian page Historikk (also by Bent Birkeland).] The first attempt to create a mathematical society in Norway was made in 1885 by Sophus Lie, who was at that time professor in Oslo. This was a time when similar initiatives took place in many European countries. Moscow Mathematical Society was founded in 1864, London in 1865, the Finnish, French and Danish ones in 1868, -72 and -73, respectively. In Norway, however, the mathematical community at that time was too small, and the venture broke down when Lie moved to Leipzig the following year. But a series of reforms in the high schools and at the university (less Latin and Greek, more modern languages, science and mathematics) during the second half of the 1800's led to a marked expansion of that community, and a formal organisation became necessary. In particular the need for a Norwegian mathematical journal was felt. The difficulty was of course to find financial support for it, and to find persons able and willing to take on the editorial work. In 1918 the time had come. Preliminary discussions took place in the early autumn. Arnfinn Palmstrøm, who at that time worked as an actuary, and from 1919 until his

55. Kurze Charakteristik Des Faches
    Translate this page von Gödel für die Arithmetik und die Logik höherer Stufe, der Nachweis der Nichtcharakterisierbarkeitder natürlichen Zahlen durch thoralf skolem und die  
    http://www-computerlabor.math.uni-kiel.de/~spinas/Logik.htm
    
    Extractions: Mathematisches Seminar Aristoteles George Boole und Gottlob Frege Die Abwehr der Antinomien, die um die Wende zum zwanzigsten Jahrhundert entdeckt wurden, war das zentrale Thema der Logik zu Beginn des zwanzigsten Jahrhunderts. Bertrand Russell Georg Cantor geschaffene Mengenlehre wurde durch die Axiomatik von Ernst Zermelo und Abraham (Adolf) Fraenkel konsolidiert. Luitzen E. Brouwer vertrat eine radikale konstruktivistische Position, nach der auf wesentliche Teile der klassischen Mathematik zu verzichten sei. Um deren Bestand durch formale Widerspruchsfreiheitsbeweise zu retten, entwickelte David Hilbert als Gegenposition das Programm der Beweistheorie. bewies und Anatolij Malcev Thoralf Skolem Alonzo Church und Alan Turing prinzipielle Grenzen aller formalen Methoden auf. Alfred Tarski beteiligt war. Heute ist die Modelltheorie eng mit klassischen mathematischen Disziplinen verwoben. Exemplarisch seien die von Abraham Robinson Thoralf Skolem John von Neumann Paul Bernays und Paul Cohen Gerhard Gentzen Alonzo Church und Alan Turing die von Stephen Kleene und Emil Post stehen.

56. Beezer's Academic Genealogy
    Albert thoralf skolem TCSGMHMBDM; Axel Thue TCSGMHM BDM;Marius Sophus Lie MHM; Peter Ludwig Mejdell Sylow MHM. The  
    http://buzzard.ups.edu/genealogy.html
    
    Extractions: 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. 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)

57. Norsk Matematisk Forening
    De som kom til å sitte lengst, var Olaf Thalberg som var med i redaksjonenfra 1921 til 1945, og thoralf skolem, med et opplag på 5600.  
    http://www.geocities.com/CapeCanaveral/Hangar/3736/nmf.htm
    
    Extractions: Det stifterne så som foreningens viktigste oppgave, var å holde god kontakt mellom de ulike matematiske miljøene i landet. Foruten universitet og skole var det særlig det forsikringstekniske miljøet og geodetene i Norges Geografiske Oppmåling som var interesserte. Man sørget da også for at det til enhver tid, i alle dall til uti 1940-årene, var personer fra alle disse miljøene i foreningens styre. La oss begynne med et par ord om hovedpersonene bak stiftelsen. Poul Heegaard (1871-1948) var dansk, hadde vært professor i København fra 1910, og var nettopp i 1918 utnevnt i et nyopprettet professorat i geometri i Oslo (byen het den gang Kristiania). I geometrien er han særlig kjent for sin doktoravhandling fra 1899, der han rydder opp i noen topologiske uklarheter i Poincarés arbeider. Heegaard-invarianter er fortsatt et nyttig begrep i topologien. Han var sterkt interessert i undervisnings- og opplysningsvirksomhet, og nedla et stort arbeid på dette området. Arnfinn Palmstrøm (1867-1922), var aktuar, og ble i 1919 professor i forsikringsmatematikk. Det var han og Heegaard som sammen gjorde det meste av forarbeidet til foreningens stiftelse. De forfattet en henvendelse til “matematikk-interesserte personer landet over” om planene for en matematisk forening, de skrev utkast til vedtekter for foreningen, og de søkte økonomisk støtte fra staten, og fra livsforsikringsselskapene.

58. Axiom Schema Of Replacement
    The axiom was independently discovered by thoralf skolem later in the same year,and it is in fact skolem s final version of the axiom list that we use today  
    http://www.fact-index.com/a/ax/axiom_schema_of_replacement.html
    
    Extractions: Main Page See live article Alphabetical index In axiomatic set theory and the branches of logic mathematics , and computer science that use it, the axiom schema of replacement is a schema of axioms in Zermelo-Fraenkel set theory Suppose P is any predicate in two variables that doesn't use the symbol B . Then in the formal language of the Zermelo-Fraenkel axioms, the axiom schema reads: or in words: Note that there is one axiom for every such predicate P ; thus, this is an axiom schema. To understand this axiom, first note that the clause in the first set of parentheses above is exactly what one needs to construct a functional predicate F in one variable such that F X Y if and only if P X Y ). Indeed, if one formalises the language of predicate logic to allow the use of derived functional predicates in axiom schemas, then the axiom schema may be rewritten as: for each derived functional predicate F in one variable; or in words:

59. Best Viewed In 24pt And Full-screen
    Translate this page skolem, Albert thoralf (Norvège, 1887-1963). skolem établit la versiondéfinitive du théorème de Löwenheim-skolem tout ensemble  
    http://www.irisa.fr/lande/ridoux/LPAZ/node62.html
    
    Extractions: Scission d'une liste de longueur paire en deux moitiés. S rel. logique combinatoire ) Combinateur de la logique combinatoire régi par l'axiome suivant. Il est définissable en -calcul et en Prolog : comb_S S :- pi x (pi y (pi z ( (S x y z) = (x z (y z)) ))) . Semi-décidable adj. rel. décidable ) Se dit d'un problème de décision pour lequel il n'existe au mieux que des procédures qui terminent toujours dans les cas de succès et peuvent ne pas terminer dans les cas d'échec. On appelle ces procédures des semi-algorithmes Séquent n. m. rel. calcul des séquents ) Assemblage de formules qui énonce que la disjonction des est une conséquence de la conjonction des . Un cas particulier intéressant est celui des séquents intuitionnistes. Ce sont les séquents où Un autre cas particulier est celui des séquents de type. Un séquent de type énonce que a le type dans le contexte . La forme exacte du contexte dépend du système de type et de sa présentation, mais il s'agit généralement d'une collection d'assertion de typage, . Par exemple, dans le cas des

60. Biography-center - Letter S
    Skoblikova, Lidiya www.olympic.org/uk/athletes/heroes/bio_uk.asp?PAR_I_ID=71478;skolem, thoralf wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/skolem  
    http://www.biography-center.com/s.html
    
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