
	Where results make sense

Topic: Thoralf Skolem

Related Topics

Spencer family

In the News (Wed 15 Feb 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Skolem (Site not responding. Last check: 2007-11-05)
		In 1909 Skolem took a job as assistant to the physicist Kristian Birkeland, who was famed for his experiments with the aurora-like effect obtained by bombarding a magnetized sphere with electrons, and Skolem's first publications were physics papers written jointly with Birkeland.
		Skolem's advisor in Kristiania (or Oslo as it was renamed in 1925) had been Axel Thue although he had died in 1922, four years before Skolem decided to submit his thesis.
		Skolem is commonly portrayed as arguing that certain otherwise well understood concepts are suspect simply because they cannot be characterized in a first-order language; in particular that, since all first-order formalizations of set theory (if consistent) have countable models, the concept of uncountability is flawed.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Skolem.html (1441 words)

	Thoralf Albert Skolem
		Thoralf Skolem was born on 23 May 1887 in Sandsvær, in the county of Buskerud in Southern Norway.
		Skolem passed his ``Examen artium'' (which is the concluding examination of the Norwegian Gymnasium) in 1905 and immediately afterwards started to study mathematics and science at the University of Oslo, where in 1913 he obtained his degree in mathematics.
		Skolem had been the first, for example, to determine the free distributive lattice generated by n elements (1913); he had shown that every implicative lattice is distributive and, as a partical converse, that every finite distributive lattice is implicative (1919).
	www.hf.uio.no /filosofi/njpl/vol1no2/skobio/node1.html (2890 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		Thoralf Skolem proved that n = 0,1 mod 4 was a necessary and sufficient condition for the existence of Skolem sequences.
		An x-dividable Skolem array is a Skolem array in which the top row is a permutation of {1,2,3...n}.
		We conjecture that in all Skolem arrays, the number of split pairs is greater than or equal to the number of unsplit pairs.
	mathcs.mta.ca /research/cbaker/skolem/results.htm (207 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		Skolem arrays are a combinatorial construct developed by Dr. C.
		Skolem arrays are an extension of Skolem sequences which were studied in the 1950s by the Norwegian mathematician Thoralf Skolem(1887-1963).
		A Skolem array of order n is a 2 × n array in which every integer i, 0 < i < n occurs exactly twice and the two occurrences are exactly i steps apart where a step is a move from the entry (a, b) to either (a+1, b) or (a, b+1).
	mathcs.mta.ca /research/cbaker/skolem (178 words)

	Skolem, Thoralf Albert (Site not responding. Last check: 2007-11-05)
		Skolem was born at Sandsvaer and educated at Oslo, where he became professor 1938.
		Skolem's main work was in the field of formal mathematical logic.
		Skolem's answer was that there is no complete axiomatization of mathematics.
	cartage.org.lb /en/themes/Biographies/MainBiographies/S/Skolem/1.html (107 words)

	Encyclopedia: LÃ¶wenheim-Skolem theorem (Site not responding. Last check: 2007-11-05)
		mathematical logic, the classic Löwenheim- Albert Thoralf Skolem (May 23, 1887 - March 23, 1963) was a Norwegian mathematician.
		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...
		The theorem is named for Leopold Löwenheim and Albert Thoralf Skolem (May 23, 1887 - March 23, 1963) was a Norwegian mathematician.
	www.nationmaster.com /encyclopedia/L%F6wenheim_Skolem-theorem (979 words)

	Albert Thoralf Skolem - netlexikon
		Durch Skolem wurde in der Axiomatisierung der Mengenlehre der Schlusspunkt gesetzt, indem er mit den Mitteln der Formalisierung dem Komprehensionsaxiom seine heute übliche Fassung gab.
		Skolem leistete ferner eine Reihe von Beträgen zum Entscheidungsproblem.
		Bücher zum Stichwort "Albert Thoralf Skolem" bei Amazon.de
	www.lexikon-definition.de /Albert-Thoralf-Skolem.html (326 words)

	Science Fair Projects - Löwenheim-Skolem theorem
		The theorem is named for Leopold Löwenheim and Thoralf Skolem.
		Since there may be many such values of y, the axiom of choice must be invoked in order to infer the existence of the Skolem function.
		Here is the idea of the proof: Start with the set of all first-order-definable members of the model, and close under all Skolem functions.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Lowenheim-Skolem_theorem (543 words)

	DMG-FG2: projects
		Skolem functions can be traced back to the famous paper by Thoralf Skolem 1920.
		Proof theoretically Skolem functions can be used to eliminate strong quantifiers and thereby to reduce Herbrand's theorem for arbitrary quantifier prefixes to its purely existential variant.
		It is of course always possible to replace strong quantifiers by Skolem functions depending on the scope of weak quantifiers (or by any other function term), the problem is how to obtain the original formula from the Skolemized version in a correct way (reSkolemization).
	www.dmg.tuwien.ac.at /fg2/index.php?id=40 (1609 words)

	[No title]
		Thoralf Skolem, "The foundations of elementary arithmetic established by means of the recursive mode of thought, without the use of apparent variables ranging over infinite domains," reprinted in From Frege to Gödel, van Heijenoort, ed., 302-333;
		Thoralf Skolem, "Some Remarks on Axiomatized Set Theory," a lecture given to the Fifth Congress of Scandinavian Mathematicians in 1922 and published in the proceedings of the Congress.
		Thoralf Skolem, "Einige Bemerkungen zu der Abhanlung von E. Zermelo: `Über die Definitheit in der Axiomatik,'" Fund.
	www.math.ucla.edu /~dam/291/mathworkshop.html (1192 words)

	References for Skolem (Site not responding. Last check: 2007-11-05)
		W Boos, Thoralf Skolem, Hermann Weyl and "Das Gefühl der Welt als begrenztes Ganzes", in From Dedekind to Gödel, Boston, MA, 1992 (Dordrecht, 1995), 283-329.
		G Gjone, Uber Leben und Werk von Thoralf Skolem, Contributions to the history, philosophy and methodology of mathematics, Wiss.
		G Mints, Thoralf Skolem and the epsilon substitution method for predicate logic, Nordic J. Philos.
	www-groups.dcs.st-and.ac.uk /~history/Printref/Skolem.html (178 words)

	Löwenheim-Skolem theorem -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-05)
		The theorem is named for (Click link for more info and facts about Leopold Löwenheim) Leopold Löwenheim and (Click link for more info and facts about Thoralf Skolem) Thoralf Skolem.
		Since there may be many such values of y, the (Click link for more info and facts about axiom of choice) axiom of choice must be invoked in order to infer the existence of the Skolem function.
		Here is the idea of the proof: Start with the set of all first-order-definable members of the model, and (The concluding part of any performance) close under all Skolem functions.
	www.absoluteastronomy.com /encyclopedia/L/L/L%F6wenheim-Skolem_theorem1.htm (320 words)

	Löwenheim Skolem theorem (Site not responding. Last check: 2007-11-05)
		In mathematical logic, the classicLöwenheim- Skolem theorem states that any "model" M has acountably infinite submodel N that satisfies exactly the same set of first-order sentences that M satisfies.
		By now the reader should begin to suspect that most mathematical structures, in particular, most members of most categories that mathematicians consider, are "models" in the sense definedhere.
		That subset of the model is the submodel whose existence the theorem asserts.
	www.therfcc.org /l%F6wenheim-skolem-theorem-76317.html (364 words)

	Skolem's Paradox and the Predestination/Free-Will Discussion (Site not responding. Last check: 2007-11-05)
		Thoralf Skolem was a mathematical logician who lived in the early part of this century, a period when Hilbert was reformulating Euclid, when Russell was reformulating Hilbert, and when Gödel was reformulating Russell.
		Skolem's theorem says that every formal system that has a model has a countable model.
		F: Just as Skolem's paradox allows for a model to be both countable and uncountable, relative to the context, so it is possible for man to have free will and also not to have free will, relative to the context of the particular instance.
	www.messiah.edu /HPAGES/FACSTAFF/CHASE/ARTICLES/skolem.htm (2810 words)

	Thoralf Skolem -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-05)
		Thoralf Skolem -- Facts, Info, and Encyclopedia article
		Albert Thoralf Skolem (May 23, 1887 - March 23, 1963) was a (A Scandinavian language that is spoken in Norway) Norwegian (A person skilled in mathematics) mathematician.
		He worked mostly on (Any logical system that abstracts the form of statements away from their content in order to establish abstract criteria of consistency and validity) mathematical logic.
	www.absoluteastronomy.com /encyclopedia/t/th/thoralf_skolem.htm (124 words)

	Thoralf Skolem (Site not responding. Last check: 2007-11-05)
		Albert Thoralf Skolem (de mayo el 23 de 1887 - de marcha la 23 de 1963) era matemático noruego.
		Skolemization, función de Skolem, formulario del normal de Skolem
		English version: Thoralf Skolem Next: Mayores Islas De Sunda Up
	www.yotor.net /wiki/es/th/Thoralf%20Skolem.htm (57 words)

	Resolution Method. Normal Forms. Skolem. Mathematical Logic. Part 5.
		Note that a formula and its Skolem normal form are not equivalent (even in the classical logic!), they are only a kind of "semi-equivalent": a set of formulas is inconsistent, iff so is the set of their Skolem normal forms.
		Skolem' s second main idea (proposed in his 1928 paper): allow introduction of new object constants and function constants.
		Since, in general, Skolem normal form is not equivalent to the initial formula, we cannot use reduction to Skolem normal forms in the usual ("positive", or affirmative) proofs.
	www.ltn.lv /~podnieks/mlog/ml5.htm (5289 words)

	Prime-factor FFT algorithm . Cooley-Tukey FFT algorithm
		Since the early 1990s, it has been widely recognized that the Internet enables broader distribution of ideas that...
		Albert Thoralf Skolem May 23, 1887 - March 23, 1963 was a Norway Norwegian mathematician.
		See: Löwenheim-Skolem theorem Skolemization, Skolem function, Skolem normal form Skolem-Noether theorem...
	www.uk.fraquisanto.net /Prime-factor_FFT_algorithm (378 words)

	Skolem (Site not responding. Last check: 2007-11-05)
		Thoralf Skolem worked on Diophantine equations, mathematical logic, group theory, lattice theory and set theory.
		He made refinements to Zermelo's axiomatic set theory, publishing work in 1922 and 1929.
		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.
	www.bg-rams.ac.at /intranet/Physik/history/Skolem.html (101 words)

	Lycos Search Results: web results for thoralf 1 thru 10 of 12,100
		JENS ERIK FENSTAD THORALF ALBERT SKOLEM 1887--1963: A BIOGRAPHICAL SKETCH...
		Thoralf Raesch - Mathematical Logic - University of Potsdam
		Thoralf Räsch Universität Potsdam Institut für Mathematik Postfach 60 15 53 D-14415 Potsdam...
	search.lycos.com /?lpv=1&loc=searchhp&query=thoralf (229 words)

	Amazon.de: English Books: From Peirce to Skolem: A Neglected Chapter in the History of Logic (Studies in the History ... (Site not responding. Last check: 2007-11-05)
		This volume is an account of the important influence on the development of mathematical logic of Charles S. Peirce and his student O.H. Mitchell, through the work of Ernst Schroder, Leopold L wenheim, and Thoralf Skolem.
		The text begins by surveying Peirce's early work, and his influence on the world of logic, going on to explore the various applications of his thought on areas of mathematics.
		Zum Seitenanfang : From Peirce to Skolem: A Neglected Chapter in the History of Logic (Studies in the History and Philosophy of Mathematics)
	www.amazon.de /exec/obidos/ASIN/044450334X (278 words)

	Beezer's Academic Genealogy (Site not responding. Last check: 2007-11-05)
		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.
		Skolem: "In the latter year [1916] he returned to Oslo, where he was made Dozent in 1918.
	buzzard.ups.edu /genealogy.html (211 words)

	Model Theory. Goedel's Completeness Theorem. Skolem's Paradox. Ramsey's Theorem. By K.Podnieks
		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.
		Thoralf Skolem): if a first order theory has a model, then it has a finite or countable model (the famous Loewenheim-Skolem theorem).
		For a formalist, Skolem's paradox is not a paradox at all.
	www.ltn.lv /~podnieks/gta.html (5980 words)

	Calixto Badesa. The Birth of Model Theory: Löwenheim's Theorem in the Frame of the Theory of Relatives Princeton: ...
		In 1920 Skolem proved the submodel version, although he stated
		With Skolem (but carefully avoiding leaning on his authority),
		Skolem functions, as I have in fact done, following van Heijenoort
	philmat.oxfordjournals.org /cgi/content/full/13/1/91 (5120 words)

	Enlaces : Science : Math : Logic_and_Foundations : History : People : Skolem,_Thoralf :: 100cia.com (Site not responding. Last check: 2007-11-05)
		Make sure the cache folder exists and is writable by this script (you may also disable the cache)
		Skolem Issue of the Nordic Journal of Philosophical Logic - Special issue with articles by Jens Erik Fenstad, Herman Ruge Jervell, Hao Wang, Grigori Mints, Matti Eklund on Skolem's life and work..
		Thoralf Skolem (1887-1963) - Biography from MacTutor History of mathematics archive..
	www.100cia.com /recursos/enlaces/Science/Math/Logic_and_Foundations/History/People/Skolem,_Thoralf (98 words)

	Teorema de Löwenheim-Skolem (Site not responding. Last check: 2007-11-05)
		El teorema se nombra para Leopold Löwenheim y Thoralf Skolem.
		Puesto que puede haber muchos tales valores de y, el axioma de la opción se debe invocar para deducir la existencia de la función de Skolem.
		Aquí está la idea de la prueba: Comenzar con el grupo de todos los miembros primero-orden-definibles del modelo, y cerrarse bajo todas las funciones de Skolem.
	www.yotor.net /wiki/es/te/Teorema%20de%20L%F6wenheimSkolem.htm (337 words)

	Skolem, Thoralf (Site not responding. Last check: 2007-11-05)
		This page was last updated on July 21st, 2005
		Skolem Issue of the Nordic Journal of Philosophical Logic
		Special issue with articles by Jens Erik Fenstad, Herman Ruge Jervell, Hao Wang, Grigori Mints, Matti Eklund on Skolem's life and work.
	www.canadiancontent.net /dir/Top/Science/Math/Logic_and_Foundations/History/People/Skolem,_Thoralf (91 words)

	The Mathematics Genealogy Project - Thoralf Skolem
		Click here to see the students listed in chronological order.
		According to our current on-line database, Thoralf Skolem has 1 students and 230 descendants.
		If you have additional information or corrections regarding this mathematician, please use the update form.
	genealogy.math.ndsu.nodak.edu /html/id.phtml?id=18237 (108 words)

	Amazon.fr : Chroniques et points de vue Livres en anglais: From Peirce to Skolem: A Neglected Chapter in the ... (Site not responding. Last check: 2007-11-05)
		From Peirce to Skolem: A Neglected Chapter in the History of Logic
		This book is an account of the important influence on the development of mathematical logic of Charles S. Peirce and his student O.H. Mitchell, through the work of Ernst Schröder, Leopold Löwenheim, and Thoralf Skolem.
		As far as we know, this book is the first work delineating this line of influence on modern mathematical logic.
	www.amazon.fr /exec/obidos/tg/detail/-/english-books/044450334X/reviews (160 words)

	the knowledge.com ™ directory - science - math - logic and foundations - history - people - skolem, thoralf
		the knowledge.com ™ directory - science - math - logic and foundations - history - people - skolem, thoralf
		home → science → math → logic and foundations → history → people → skolem, thoralf
		Help build the largest human-edited directory on the web.
	directory.knowledge.com /science/math/logic_and_foundations/history/people/skolem,_thoralf (103 words)

Try your search on: Qwika (all wikis)