- elementarily equivalent structures
- Математика: элементарно эквивалентные структуры
Универсальный англо-русский словарь. Академик.ру. 2011.
elementarily equivalent structures
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Elementarily equivalent — In mathematics, specifically model theory, two structures for a given language are said to be elementarily equivalent if any sentence satisfied by one model is also satisfied by the other. Relationship to complete theories If T is a consistent… … Wikipedia
metalogic — /met euh loj ik/, n. the logical analysis of the fundamental concepts of logic. [1835 45; META + LOGIC] * * * Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal… … Universalium
Model theory — This article is about the mathematical discipline. For the informal notion in other parts of mathematics and science, see Mathematical model. In mathematics, model theory is the study of (classes of) mathematical structures (e.g. groups, fields,… … Wikipedia
Absoluteness (mathematical logic) — In mathematical logic, a formula is said to be absolute if it has the same truth value in each of some class of structures (also called models). Theorems about absoluteness typically show that each of a large syntactic class of formulas is… … Wikipedia
o-minimal theory — In mathematical logic, and more specifically in model theory, an infinite structure (M,<,...) which is totally ordered by < is called an o minimal structure if and only if every definable subset X ⊂ M (with parameters taken from… … Wikipedia
Mathematical logic — (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… … Wikipedia
List of first-order theories — In mathematical logic, a first order theory is given by a set of axioms in somelanguage. This entry lists some of the more common examples used in model theory and some of their properties. PreliminariesFor every natural mathematical structure… … Wikipedia
Elementary substructure — In model theory, given two structures mathfrak A 0 and mathfrak A, both of a common signature Sigma, we say that mathfrak A 0 is an elementary substructure of mathfrak A (sometimes notated mathfrak A 0 preceq mathfrak A [Monk 1976: 331 (= Def. 19 … Wikipedia
Ehrenfeucht–Fraïssé game — In the mathematical discipline of model theory, the Ehrenfeucht Fraïssé game is a technique for determining whether two structures are elementarily equivalent. The main application of Ehrenfeucht Fraïssé games is in proving the inexpressibility… … Wikipedia
Roland Fraïssé — (born 1920; died Marseille, March 30, 2008 [ [http://www.site.uottawa.ca/ lrakotom/rogics2008/RolandFraisse.html Rogics08 Deces de Roland Fraisse Message de Maurice Pouzet et Gerard Lopez] , accessed May 22, 2008.] ) was a French mathematical… … Wikipedia
Interpretation (logic) — An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until … Wikipedia
