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elementarily equivalent

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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

  • Prime model — In mathematics, and in particular model theory, a prime model is a model which is as simple as possible. Specifically, a model P is prime if it admits an elementary embedding into any model M to which it is elementarily equivalent (that is, into… …   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

  • Zlil Sela — is an Isareli mathematician working in the area of geometric group theory.He is a Professor of Mathematics at the Hebrew University of Jerusalem. Sela is known for the solution of the isomorphism problem for torsion free word hyperbolic groups… …   Wikipedia

  • 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

  • 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

  • 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 mathematics articles (E) — NOTOC E E₇ E (mathematical constant) E function E₈ lattice E₈ manifold E∞ operad E7½ E8 investigation tool Earley parser Early stopping Earnshaw s theorem Earth mover s distance East Journal on Approximations Eastern Arabic numerals Easton s… …   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

  • 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

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