Thoralf Albert Skolem (Norwegian: [ˈtûːrɑɫf ˈskûːlɛm]; 23 May 1887 – 23 March 1963) was a Norwegian mathematician who worked in mathematical logic and...

In mathematical logic and philosophy, Skolem's paradox is the apparent contradiction that a countable model of first-order set theory could contain an...

the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf Skolem. The precise formulation...

Skolem normal form if it is in prenex normal form with only universal first-order quantifiers. Every first-order formula may be converted into Skolem...

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...

Skolem arithmetic is the first-order theory of the natural numbers with multiplication, named in honor of Thoralf Skolem. The signature of Skolem arithmetic...

that make it amenable to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem. First-order logic is the standard for...

In ring theory, a branch of mathematics, the Skolem–Noether theorem characterizes the automorphisms of simple rings. It is a fundamental result in the...

Skolem arithmetic may refer to several distinct types of arithmetic. Skolem arithmetic, the arithmetic of positive number with multiplication and equality...

Langford pairings for a given value of n. The closely related concept of a Skolem sequence is defined in the same way, but instead permutes the sequence 0...

whose operational meaning was not clear. In 1922, Fraenkel and Thoralf Skolem independently proposed operationalizing a "definite" property as one that...

In mathematics, in the field of number theory, the Ramanujan–Nagell equation is an equation between a square number and a number that is seven less than...

Löwenheim (1915) gave the first proof of what is now known as the Löwenheim–Skolem theorem, often considered the starting point for model theory. Leopold was...

formula. Thoralf Skolem had considered the Skolemizations of formulas in prenex form as part of his proof of the Löwenheim–Skolem theorem (Skolem 1920). Herbrand...

Thoralf Skolem obtained the Löwenheim–Skolem theorem, which says that first-order logic cannot control the cardinalities of infinite structures. Skolem realized...

In additive and algebraic number theory, the Skolem–Mahler–Lech theorem states that if a sequence of numbers satisfies a linear difference equation, then...

advanced research lead to the modernisation of crypto-algorithms. Thoralf Skolem made revolutionary contributions to mathematical logic. Øystein Ore and...

cornerstone of first-order model theory is the Löwenheim-Skolem theorem. According to the Löwenheim-Skolem Theorem, every infinite structure in a countable signature...

theorem is one of the two key properties, along with the downward Löwenheim–Skolem theorem, that is used in Lindström's theorem to characterize first-order...

review of Skolem's paper, in which Fraenkel simply stated that Skolem's considerations correspond to his own. Zermelo himself never accepted Skolem's formulation...

carry over to second-order logic with Henkin semantics. Since also the Skolem–Löwenheim theorems hold for Henkin semantics, Lindström's theorem imports...

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...

elementarily equivalent models, which can be obtained via the Löwenheim–Skolem theorem. Thus, for example, there are non-standard models of Peano arithmetic...

automation. In 1920, Thoralf Skolem simplified a previous result by Leopold Löwenheim, leading to the Löwenheim–Skolem theorem and, in 1930, to the notion...

S3. 1920 - Thoralf Skolem proves the (downward) Löwenheim-Skolem theorem using the axiom of choice explicitly. 1922 - Thoralf Skolem proves a weaker version...

 paradox and diagonal argument Compactness Halting problem Lindström's Löwenheim–Skolem Russell's paradox Logics Set theory Formal systems (list), language and syntax...

criterion" is imprecise, and is fixed by Weyl, Fraenkel, Skolem, and von Neumann. In fact Skolem in his 1922 referred to this "definite criterion" or "property"...

+1}[A]\subseteq M_{\lambda }[(A\cap \lambda )\cup H]\cup \{\lambda \}} Skolem property. If α {\displaystyle \alpha } is *definable from the set X ⊆ O...

Mathematicians such as Gottlob Frege, Ernst Zermelo, Abraham Fraenkel, and Thoralf Skolem put much effort into revising set theory to eliminate these contradictions...

Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo...