The ultraproduct is a mathematical construction that appears mainly in abstract algebra and mathematical logic, in particular in model theory and set theory...
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numbers. The ultraproduct models are uncountable. One way to see this is to construct an injection of the infinite product of N into the ultraproduct. However...
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Model theory (section Ultraproducts)
hypothesis holds. Ultraproducts are used as a general technique for constructing models that realise certain types. An ultraproduct is obtained from the...
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Kripke's T-schema Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably...
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constructions. For example, an ultraproduct modulo a principal ultrafilter is always isomorphic to one of the factors, while an ultraproduct modulo a free ultrafilter...
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\varphi } holds in the ultraproduct ∏ i ⊆ Σ M i / U . {\textstyle \prod _{i\subseteq \Sigma }{\mathcal {M}}_{i}/U.} So this ultraproduct satisfies all formulas...
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Kripke's T-schema Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably...
41 KB (5,016 words) - 11:36, 2 September 2024
Kripke's T-schema Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably...
74 KB (9,526 words) - 14:50, 20 August 2024
to two fields, one given by an ultraproduct over all primes of the fields Fp((t)) and the other given by an ultraproduct over all primes of the p-adic...
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reduced product is a construction that generalizes both direct product and ultraproduct. Let {Si | i ∈ I} be a nonempty family of structures of the same signature...
2 KB (280 words) - 21:05, 26 September 2023