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

from part of the Löwenheim–Skolem theorem; Thoralf Skolem was the first to discuss the seemingly contradictory aspects of the theorem, and to discover...

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

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

the downward Löwenheim–Skolem theorem, published by Leopold Löwenheim in 1915. The compactness theorem was implicit in work by Thoralf Skolem, but it was...

greatly simplified the proof of a theorem Leopold Löwenheim first proved in 1915, resulting in the Löwenheim–Skolem theorem, which states that if a countable...

resumed teaching mathematics. Löwenheim (1915) gave the first proof of what is now known as the Löwenheim–Skolem theorem, often considered the starting...

model theory is the Löwenheim–Skolem theorem, which can be proven via Skolemizing the theory and closing under the resulting Skolem functions. In general...

independence results in set theory. Leopold Löwenheim and Thoralf Skolem obtained the Löwenheim–Skolem theorem, which says that first-order logic cannot...

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

subsets of the domain. It follows from the compactness theorem and the upward Löwenheim–Skolem theorem that it is not possible to characterize finiteness...

mathematical logic the Löwenheim number of an abstract logic is the smallest cardinal number for which a weak downward Löwenheim–Skolem theorem holds. They are...

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

models are isomorphic. It follows from the definition above and the Löwenheim–Skolem theorem that any first-order theory with a model of infinite cardinality...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

Löwenheim–Skolem theorem, says: Every syntactically consistent, countable first-order theory has a finite or countable model. Given Henkin's theorem,...

(countable) compactness property and the (downward) Löwenheim–Skolem property. Lindström's theorem is perhaps the best known result of what later became...

undefinability theorem Church-Turing theorem of undecidability Löb's theorem Löwenheim–Skolem theorem Lindström's theorem Craig's theorem Cut-elimination theorem The...

\varphi } . The following lemma, which Gödel adapted from Skolem's proof of the Löwenheim–Skolem theorem, lets us sharply reduce the complexity of the generic...

{\displaystyle \Rightarrow } Löwenheim–Skolem theorem" — that is, D C {\displaystyle {\mathsf {DC}}} implies the Löwenheim–Skolem theorem. See table Moore, Gregory...

infinite model; this affects the statements of results such as the Löwenheim–Skolem theorem, which are usually stated under the assumption that only normal...

Cantor's contradictions. 1915 - Leopold Löwenheim publishes a proof of the (downward) Löwenheim-Skolem theorem, implicitly using the axiom of choice. 1918...

logic) Lindström's theorem (mathematical logic) Löb's theorem (mathematical logic) Łoś' theorem (model theory) Löwenheim–Skolem theorem (mathematical logic)...

propertiesPages displaying wikidata descriptions as a fallback Löwenheim–Skolem theorem – Existence and cardinality of models of logical theories Transfer...

necessitates the truth of another. downward Löwenheim–Skolem theorem Part of the Löwenheim–Skolem theorem. doxastic modal logic A branch of modal logic...

compactness theorem implies that the existence of nonstandard elements cannot be excluded in first-order logic. The upward Löwenheim–Skolem theorem shows that...

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...

z_{i}} drawn from L β {\displaystyle L_{\beta }} . By the downward Löwenheim–Skolem theorem and Mostowski collapse, there must be some transitive set K {\displaystyle...

properties as axioms requires the use of second-order logic. The Löwenheim–Skolem theorems tell us that if we restrict ourselves to first-order logic, any...

possible to characterize the reals with first-order logic alone: the Löwenheim–Skolem theorem implies that there exists a countable dense subset of the real...