logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf Skolem. The precise...
22 KB (2,767 words) - 08:16, 16 March 2024
logic and philosophy, Skolem's paradox is a seeming contradiction that arises from the downward Löwenheim–Skolem theorem. Thoralf Skolem (1922) was the first...
18 KB (2,433 words) - 11:52, 20 March 2024
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...
14 KB (1,948 words) - 18:48, 19 January 2024
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...
12 KB (1,513 words) - 19:38, 22 January 2024
model theory is the Löwenheim–Skolem theorem, which can be proven via Skolemizing the theory and closing under the resulting Skolem functions. In general...
11 KB (1,907 words) - 17:35, 15 April 2024
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...
93 KB (13,173 words) - 20:30, 24 April 2024
resumed teaching mathematics. Löwenheim (1915) gave the first proof of what is now known as the Löwenheim–Skolem theorem, often considered the starting...
7 KB (467 words) - 21:01, 25 April 2024
automatisation. In 1920, Thoralf Skolem simplified a previous result by Leopold Löwenheim, leading to the Löwenheim–Skolem theorem and, in 1930, to the notion...
28 KB (2,891 words) - 23:29, 10 February 2024
independence results in set theory. Leopold Löwenheim and Thoralf Skolem obtained the Löwenheim–Skolem theorem, which says that first-order logic cannot...
68 KB (8,329 words) - 19:55, 6 May 2024
cornerstone of first-order model theory is the Löwenheim-Skolem theorem. According to the Löwenheim-Skolem Theorem, every infinite structure in a countable...
62 KB (9,082 words) - 07:39, 8 May 2024
subsets of the domain. It follows from the compactness theorem and the upward Löwenheim–Skolem theorem that it is not possible to characterize finiteness...
31 KB (4,321 words) - 11:40, 19 February 2024
Löwenheim–Skolem theorem, says: Every syntactically consistent, countable first-order theory has a finite or countable model. Given Henkin's theorem,...
17 KB (2,329 words) - 06:10, 20 May 2024
elementarily equivalent models, which can be obtained via the Löwenheim–Skolem theorem. Thus, for example, there are non-standard models of Peano arithmetic...
8 KB (956 words) - 00:42, 21 September 2023
undefinability theorem Church-Turing theorem of undecidability Löb's theorem Löwenheim–Skolem theorem Lindström's theorem Craig's theorem Cut-elimination theorem The...
34 KB (4,373 words) - 07:13, 25 December 2023
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...
10 KB (1,151 words) - 08:29, 7 March 2024
{\displaystyle \Rightarrow } Löwenheim–Skolem theorem" — that is, D C {\displaystyle {\mathsf {DC}}} implies the Löwenheim–Skolem theorem. See table Moore, Gregory...
9 KB (947 words) - 10:00, 14 May 2024
of the natural numbers (Cantor's theorem 1891) Löwenheim–Skolem theorem (Leopold Löwenheim 1915 and Thoralf Skolem 1919) Proof of the consistency of...
11 KB (1,388 words) - 04:04, 19 May 2024
Soundness theorem Gödel's completeness theorem Original proof of Gödel's completeness theorem Compactness theorem Löwenheim–Skolem theorem Skolem's paradox...
14 KB (1,012 words) - 19:53, 12 November 2023
infinite model; this affects the statements of results such as the Löwenheim–Skolem theorem, which are usually stated under the assumption that only normal...
32 KB (4,421 words) - 20:08, 14 February 2024
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...
5 KB (654 words) - 04:46, 20 March 2024
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...
92 KB (12,120 words) - 13:48, 13 May 2024
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...
32 KB (6,092 words) - 02:09, 31 December 2023
\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...
26 KB (4,798 words) - 01:47, 19 April 2024
necessitates the truth of another. downward Löwenheim–Skolem theorem Part of the Löwenheim–Skolem theorem. doxastic modal logic A branch of modal logic...
266 KB (29,838 words) - 06:24, 12 May 2024
the infinite product of N into the ultraproduct. However, by the Löwenheim–Skolem theorem there must exist countable non-standard models of arithmetic. One...
10 KB (1,275 words) - 21:48, 27 December 2023
theorem (number theory) Looman–Menchoff theorem (complex analysis) Łoś' theorem (model theory) Lovelock's theorem (physics) Löwenheim–Skolem theorem (mathematical...
73 KB (5,996 words) - 17:15, 5 May 2024
(countable) compactness property and the (downward) Löwenheim–Skolem property. Lindström's theorem is perhaps the best known result of what later became...
4 KB (386 words) - 20:20, 15 January 2022
algebra Abstract model theory Löwenheim number – smallest cardinal number for which a weak downward Löwenheim–Skolem theorem holdsPages displaying wikidata...
1 KB (145 words) - 02:56, 12 December 2023
1920: Thoralf Skolem corrected Leopold Löwenheim's proof of what is now called the downward Löwenheim–Skolem theorem, leading to Skolem's paradox discussed...
47 KB (6,198 words) - 06:36, 31 March 2024
Grelling's, that absolute generality leads to indeterminacy due to the Löwenheim–Skolem theorem, or that absolute generality fails because the notion of "object"...
3 KB (306 words) - 07:47, 27 April 2024