• Thumbnail for Thoralf Skolem
    Thoralf Albert Skolem (Norwegian: [ˈtùːrɑɫf ˈskùːlɛm]; 23 May 1887 – 23 March 1963) was a Norwegian mathematician who worked in mathematical logic and...
    12 KB (1,513 words) - 19:38, 22 January 2024
  • the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf Skolem. The precise formulation...
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  • is an atomic prime model over A. Skolem normal form is named after the late Norwegian mathematician Thoralf Skolem. Herbrandization, the dual of Skolemization...
    11 KB (1,907 words) - 17:35, 15 April 2024
  • logic and philosophy, Skolem's paradox is a seeming contradiction that arises from the downward Löwenheim–Skolem theorem. Thoralf Skolem (1922) was the first...
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  • the logical language itself. The language of ZFC, with the help of Thoralf Skolem, turned out to be that of first-order logic. Most sets commonly encountered...
    31 KB (4,602 words) - 15:51, 18 April 2024
  • theory of central simple algebras. The theorem was first published by Thoralf Skolem in 1927 in his paper Zur Theorie der assoziativen Zahlensysteme (German:...
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  • Skolem arithmetic is the first-order theory of the natural numbers with multiplication, named in honor of Thoralf Skolem. The signature of Skolem arithmetic...
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  • in Economic History Thoralf Sandaker (born 1923), Norwegian former rower who competed in the 1948 Summer Olympics Thoralf Skolem (1887–1963), Norwegian...
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  • zero form a regularly repeating pattern. This result is named after Thoralf Skolem (who proved the theorem for sequences of rational numbers), Kurt Mahler...
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  • values F(0) = 0 and F(1) = 1. The Skolem problem is named after Thoralf Skolem, because of his 1933 paper proving the Skolem–Mahler–Lech theorem on the zeros...
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  • itself a set. The preceding form of separation was introduced in 1930 by Thoralf Skolem as a refinement of a previous, non-first-order form by Zermelo. The...
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  • Thumbnail for Infinitesimal
    Émile Borel and Thoralf Skolem. Borel explicitly linked du Bois-Reymond's work to Cauchy's work on rates of growth of infinitesimals. Skolem developed the...
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  • Proceedings of Symposia in Pure Mathematics Volume 13, Part II, pp. 207–214 Skolem, Thoralf (1923), Axiomatized set theory Reprinted in From Frege to Gödel, van...
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  • Thumbnail for Cardinality
    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo...
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  • unique function. Primitive recursive arithmetic was first proposed by Thoralf Skolem in 1923. The current terminology was coined by Rózsa Péter (1934) after...
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  • property, whose operational meaning was not clear. In 1922, Fraenkel and Thoralf Skolem independently proposed operationalizing a "definite" property as one...
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  • theory (ZFC). The axiom was independently discovered and announced by Thoralf Skolem later in the same year (and published in 1923). Zermelo himself incorporated...
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  • German mathematician Leopold Löwenheim (1915) the Norwegian logician Thoralf Skolem showed in 1922 that every consistent theory of first-order predicate...
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  • early as 1923 by Skolem, even before Gödel's first incompleteness theorem. Skolem argued on the basis of what is now known as Skolem's paradox, and it...
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  • outside this initial segment. The construction of such models is due to Thoralf Skolem (1934). Non-standard models of arithmetic exist only for the first-order...
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  • formula. Thoralf Skolem had considered the Skolemizations of formulas in prenex form as part of his proof of the Löwenheim–Skolem theorem (Skolem 1920)....
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  • Thumbnail for Complement (set theory)
    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo...
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  • Thumbnail for Cartesian product
    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo...
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  • Thumbnail for Union (set theory)
    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo...
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  • Thumbnail for Intersection (set theory)
    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo...
    12 KB (1,737 words) - 23:16, 26 December 2023
  • automatisation. In 1920, Thoralf Skolem simplified a previous result by Leopold Löwenheim, leading to the Löwenheim–Skolem theorem and, in 1930, to the...
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  • Thumbnail for Ernst Zermelo
    axioms, with the original numbering. In 1922, Abraham Fraenkel and Thoralf Skolem independently improved Zermelo's axiom system. The resulting system...
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  • Thumbnail for Subset
    Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo...
    11 KB (1,631 words) - 08:10, 28 April 2024
  • Thumbnail for Axel Thue
    closely related to the halting problem. His only known PhD student was Thoralf Skolem. The esoteric programming language Thue is named after him. Thue, A...
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  • Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo...
    17 KB (2,416 words) - 16:31, 10 February 2024