Definition of Ultraproduct. Meaning of Ultraproduct. Synonyms of Ultraproduct

- The ultraproduct is a mathematical construction that appears mainly in abstract algebra and mathematical logic, in particular in model theory and set theory...
- hypothesis holds. Ultraproducts are used as a general technique for constructing models that realise certain types. An ultraproduct is obtained from the...
- 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...
- constructions. For example, an ultraproduct modulo a prin****l ultrafilter is always isomorphic to one of the factors, while an ultraproduct modulo a free ultrafilter...
- any first-order formula is true in an ultraproduct if and only if it is true in "most" factors (see ultraproduct for details). In model theory he also...
- is an ultrafilter on a set I, and Fi is a field for every i in I, the ultraproduct of the Fi with respect to U is a field. It is denoted by ulimi→∞ Fi,...
- is an initially subamenable graph, or equivalently a subgroup of an ultraproduct of finite-rank symmetric groups such that every two elements of the group...
- compact Hausdorff spaces, and in model theory in the construction of ultraproducts and ultrapowers. Every ultrafilter on a compact Hausdorff space converges...
- \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...
- product category, a category that is the product of categories. the ultraproduct, in model theory. the internal product of a monoidal category, which...