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elementary equivalence

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  • 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

  • Row equivalence — In linear algebra, two matrices are row equivalent if one can be changed to the other by a sequence of elementary row operations. Alternatively, two m times; n matrices are row equivalent if and only if they have the same row space. The concept… …   Wikipedia

  • Matrix equivalence — In linear algebra, two rectangular m by n matrices A and B are called equivalent if for some invertible n by n matrix P and some invertible m by m matrix Q. Equivalent matrices represent the same linear transformation V → W under two… …   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

  • List of philosophy topics (D-H) — DDaDai Zhen Pierre d Ailly Jean Le Rond d Alembert John Damascene Damascius John of Damascus Peter Damian Danish philosophy Dante Alighieri Arthur Danto Arthur C. Danto Arthur Coleman Danto dao Daodejing Daoism Daoist philosophy Charles Darwin… …   Wikipedia

  • Potential isomorphism — In mathematical logic and in particular in model theory, a potential isomorphism is a collection of finite partial isomorphisms between two models which satisfies certain closure conditions. Existence of a partial isomorphism entails elementary… …   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

  • Principia Mathematica — For Isaac Newton s book containing basic laws of physics, see Philosophiæ Naturalis Principia Mathematica. The title page of the shortened version of the Principia Mathematica to *56. The Principia Mathematica is a three volume work on 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

  • General relativity — For a generally accessible and less technical introduction to the topic, see Introduction to general relativity. General relativity Introduction Mathematical formulation Resources …   Wikipedia

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