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- Elementary_equivalence abstract "In model theory, a branch of mathematical logic, two structures M and N of the same signature σ are called elementarily equivalent if they satisfy the same first-order σ-sentences.If N is a substructure of M, one often needs a stronger condition. In this case N is called an elementary substructure of M if every first-order σ-formula φ(a1, …, an) with parameters a1, …, an from N is true in N if and only if it is true in M.If N is an elementary substructure of M, M is called an elementary extension of N. An embedding h: N → M is called an elementary embedding of N into M if h(N) is an elementary substructure of M.A substructure N of M is elementary if and only if it passes the Tarski–Vaught test: every first-order formula φ(x, b1, …, bn) with parameters in N that has a solution in M also has a solution in N when evaluated in M. One can prove that two structures are elementary equivalent with the Ehrenfeucht–Fraïssé games.".
- Elementary_equivalence wikiPageID "972601".
- Elementary_equivalence wikiPageLength "7160".
- Elementary_equivalence wikiPageOutDegree "27".
- Elementary_equivalence wikiPageRevisionID "655373914".
- Elementary_equivalence wikiPageWikiLink Cambridge_University_Press.
- Elementary_equivalence wikiPageWikiLink Category:Model_theory.
- Elementary_equivalence wikiPageWikiLink Complete_theory.
- Elementary_equivalence wikiPageWikiLink Critical_point_(set_theory).
- Elementary_equivalence wikiPageWikiLink Ehrenfeucht–Fraïssé_game.
- Elementary_equivalence wikiPageWikiLink Ehrenfeucht–Fraïssé_games.
- Elementary_equivalence wikiPageWikiLink Embedding.
- Elementary_equivalence wikiPageWikiLink First-order_logic.
- Elementary_equivalence wikiPageWikiLink Large_cardinal.
- Elementary_equivalence wikiPageWikiLink Large_cardinals.
- Elementary_equivalence wikiPageWikiLink Linear_ordering.
- Elementary_equivalence wikiPageWikiLink Löwenheim–Skolem_theorem.
- Elementary_equivalence wikiPageWikiLink Mathematical_logic.
- Elementary_equivalence wikiPageWikiLink Model_theory.
- Elementary_equivalence wikiPageWikiLink Morleys_categoricity_theorem.
- Elementary_equivalence wikiPageWikiLink Non-standard_model_of_arithmetic.
- Elementary_equivalence wikiPageWikiLink Peano_arithmetic.
- Elementary_equivalence wikiPageWikiLink Peano_axioms.
- Elementary_equivalence wikiPageWikiLink Rational_number.
- Elementary_equivalence wikiPageWikiLink Rational_numbers.
- Elementary_equivalence wikiPageWikiLink Real_number.
- Elementary_equivalence wikiPageWikiLink Real_numbers.
- Elementary_equivalence wikiPageWikiLink Set_theory.
- Elementary_equivalence wikiPageWikiLink Signature_(logic).
- Elementary_equivalence wikiPageWikiLink Signature_(mathematical_logic).
- Elementary_equivalence wikiPageWikiLink Structure_(mathematical_logic).
- Elementary_equivalence wikiPageWikiLink Substructure.
- Elementary_equivalence wikiPageWikiLink Theory_(mathematical_logic).
- Elementary_equivalence wikiPageWikiLink Total_order.
- Elementary_equivalence wikiPageWikiLink Vaughts_test.
- Elementary_equivalence wikiPageWikiLink Σ-sentence.
- Elementary_equivalence wikiPageWikiLinkText "1-elementary submodel".
- Elementary_equivalence wikiPageWikiLinkText "Elementary equivalence".
- Elementary_equivalence wikiPageWikiLinkText "Elementary equivalence#Elementary embeddings".
- Elementary_equivalence wikiPageWikiLinkText "elementary embedding".
- Elementary_equivalence wikiPageWikiLinkText "elementary substructure".
- Elementary_equivalence hasPhotoCollection Elementary_equivalence.
- Elementary_equivalence wikiPageUsesTemplate Template:Citation.
- Elementary_equivalence wikiPageUsesTemplate Template:Exist.
- Elementary_equivalence subject Category:Model_theory.
- Elementary_equivalence hypernym Substructure.
- Elementary_equivalence comment "In model theory, a branch of mathematical logic, two structures M and N of the same signature σ are called elementarily equivalent if they satisfy the same first-order σ-sentences.If N is a substructure of M, one often needs a stronger condition.".
- Elementary_equivalence label "Elementary equivalence".
- Elementary_equivalence sameAs Elementární_vnoření.
- Elementary_equivalence sameAs Elementare_Äquivalenz.
- Elementary_equivalence sameAs Rudimenta_enigo.
- Elementary_equivalence sameAs Équivalence_élémentaire.
- Elementary_equivalence sameAs Equivalenza_elementare.
- Elementary_equivalence sameAs 기본_동치.
- Elementary_equivalence sameAs Equivalência_elementar.
- Elementary_equivalence sameAs m.03vmkz.
- Elementary_equivalence sameAs Elementär_ekvivalens.
- Elementary_equivalence sameAs Q877149.
- Elementary_equivalence sameAs Q877149.
- Elementary_equivalence sameAs 初等等价.
- Elementary_equivalence wasDerivedFrom Elementary_equivalence?oldid=655373914.
- Elementary_equivalence isPrimaryTopicOf Elementary_equivalence.