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

logic and philosophy, Skolem's paradox is a seeming contradiction that arises from the downward Löwenheim–Skolem theorem. Thoralf Skolem (1922) was the first...

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...

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

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...

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...

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

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

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

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

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

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

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

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...

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

of the natural numbers (Cantor's theorem 1891) Löwenheim–Skolem theorem (Leopold Löwenheim 1915 and Thoralf Skolem 1919) Proof of the consistency of...

Soundness theorem Gödel's completeness theorem Original proof of Gödel's completeness theorem Compactness theorem Löwenheim–Skolem theorem Skolem's paradox...

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

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...

This set is called the minimal model of ZFC. Using the downward Löwenheim–Skolem theorem, one can show that the minimal model (if it exists) is a countable...

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

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

the infinite product of N into the ultraproduct. However, by the Löwenheim–Skolem theorem there must exist countable non-standard models of arithmetic. One...

\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...

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

algebra Abstract model theory Löwenheim number – smallest cardinal number for which a weak downward Löwenheim–Skolem theorem holdsPages displaying wikidata...

theorem Gödel's second incompleteness theorem Independence (mathematical logic) Logical consequence Löwenheim–Skolem theorem Metalanguage Metasyntactic variable...

theorem (number theory) Looman–Menchoff theorem (complex analysis) Łoś' theorem (model theory) Lovelock's theorem (physics) Löwenheim–Skolem theorem (mathematical...

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