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...

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...

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

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

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...

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

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...

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

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...

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

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...

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

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...

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

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...

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

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

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

model theory Löwenheim number – Smallest cardinal number for which a weak downward Löwenheim–Skolem theorem holds Lindström's theorem – Theorem in mathematical...

a type of Turing machine used for log-space reductions Löwenheim–Skolem theorem, a theorem in first-order logic dealing with the cardinality of models...

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

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

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

chip Land Surveyor Least squares, a regression analysis Löwenheim–Skolem theorem, a theorem in first-order logic dealing with the cardinality of models...

prime models are restricted to very specific cardinalities by the Löwenheim–Skolem theorem. If L {\displaystyle L} is a first-order language with cardinality...