logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf Skolem. The precise...
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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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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...
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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...
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model theory is the Löwenheim–Skolem theorem, which can be proven via Skolemizing the theory and closing under the resulting Skolem functions. In general...
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resumed teaching mathematics. Löwenheim (1915) gave the first proof of what is now known as the Löwenheim–Skolem theorem, often considered the starting...
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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...
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automatisation. In 1920, Thoralf Skolem simplified a previous result by Leopold Löwenheim, leading to the Löwenheim–Skolem theorem and, in 1930, to the notion...
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cornerstone of first-order model theory is the Löwenheim-Skolem theorem. According to the Löwenheim-Skolem Theorem, every infinite structure in a countable...
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independence results in set theory. Leopold Löwenheim and Thoralf Skolem obtained the Löwenheim–Skolem theorem, which says that first-order logic cannot...
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subsets of the domain. It follows from the compactness theorem and the upward Löwenheim–Skolem theorem that it is not possible to characterize finiteness...
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elementarily equivalent models, which can be obtained via the Löwenheim–Skolem theorem. Thus, for example, there are non-standard models of Peano arithmetic...
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Categorical theory (redirect from Morley categoricity theorem)
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...
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{\displaystyle \Rightarrow } Löwenheim–Skolem theorem" — that is, D C {\displaystyle {\mathsf {DC}}} implies the Löwenheim–Skolem theorem. See table Moore, Gregory...
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Löwenheim–Skolem theorem, says: Every syntactically consistent, countable first-order theory has a finite or countable model. Given Henkin's theorem,...
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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...
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undefinability theorem Church-Turing theorem of undecidability Löb's theorem Löwenheim–Skolem theorem Lindström's theorem Craig's theorem Cut-elimination theorem The...
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necessitates the truth of another. downward Löwenheim–Skolem theorem Part of the Löwenheim–Skolem theorem. doxastic modal logic A branch of modal logic...
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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...
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Soundness theorem Gödel's completeness theorem Original proof of Gödel's completeness theorem Compactness theorem Löwenheim–Skolem theorem Skolem's paradox...
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of the natural numbers (Cantor's theorem 1891) Löwenheim–Skolem theorem (Leopold Löwenheim 1915 and Thoralf Skolem 1919) Proof of the consistency of...
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infinite model; this affects the statements of results such as the Löwenheim–Skolem theorem, which are usually stated under the assumption that only normal...
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most f(φ). In other words, there is no effective analogue to the Löwenheim–Skolem theorem in the finite. This proof is taken from Chapter 10, section 4,...
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the infinite product of N into the ultraproduct. However, by the Löwenheim–Skolem theorem there must exist countable non-standard models of arithmetic. One...
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(countable) compactness property and the (downward) Löwenheim–Skolem property. Lindström's theorem is perhaps the best known result of what later became...
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\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...
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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). Herbrand...
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Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...
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Cantor's contradictions. 1915 - Leopold Löwenheim publishes a proof of the (downward) Löwenheim-Skolem theorem, implicitly using the axiom of choice. 1918...
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1920: Thoralf Skolem corrected Leopold Löwenheim's proof of what is now called the downward Löwenheim–Skolem theorem, leading to Skolem's paradox discussed...
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