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- Compactness_theorem abstract "In mathematical logic, the compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important tool in model theory, as it provides a useful method for constructing models of any set of sentences that is finitely consistent. The compactness theorem for the propositional calculus is a consequence of Tychonoff's theorem (which says that the product of compact spaces is compact) applied to compact Stone spaces; hence, the theorem's name. Likewise, it is analogous to the finite intersection property characterization of compactness in topological spaces: a collection of closed sets in a compact space has a non-empty intersection if every finite subcollection has a non-empty intersection.The compactness theorem is one of the two key properties, along with the downward Löwenheim–Skolem theorem, that is used in Lindström's theorem to characterize first-order logic. Although there are some generalizations of the compactness theorem to non-first-order logics, the compactness theorem itself does not hold in them.".
- Compactness_theorem wikiPageID "152207".
- Compactness_theorem wikiPageLength "9071".
- Compactness_theorem wikiPageOutDegree "42".
- Compactness_theorem wikiPageRevisionID "618826157".
- Compactness_theorem wikiPageWikiLink Anatoly_Maltsev.
- Compactness_theorem wikiPageWikiLink Axiom_of_choice.
- Compactness_theorem wikiPageWikiLink Barwise_compactness_theorem.
- Compactness_theorem wikiPageWikiLink Boolean_prime_ideal_theorem.
- Compactness_theorem wikiPageWikiLink Cambridge_University_Press.
- Compactness_theorem wikiPageWikiLink Cardinal_number.
- Compactness_theorem wikiPageWikiLink Cardinality.
- Compactness_theorem wikiPageWikiLink Category:Metatheorems.
- Compactness_theorem wikiPageWikiLink Category:Model_theory.
- Compactness_theorem wikiPageWikiLink Category:Theorems_in_the_foundations_of_mathematics.
- Compactness_theorem wikiPageWikiLink Characteristic_(algebra).
- Compactness_theorem wikiPageWikiLink Compact_space.
- Compactness_theorem wikiPageWikiLink Consistency.
- Compactness_theorem wikiPageWikiLink Elsevier.
- Compactness_theorem wikiPageWikiLink Field_(mathematics).
- Compactness_theorem wikiPageWikiLink Filter_(mathematics).
- Compactness_theorem wikiPageWikiLink Finite_intersection_property.
- Compactness_theorem wikiPageWikiLink First-order_logic.
- Compactness_theorem wikiPageWikiLink First-order_predicate_calculus.
- Compactness_theorem wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Compactness_theorem wikiPageWikiLink Gxc3xb6dels_completeness_theorem.
- Compactness_theorem wikiPageWikiLink Herbrands_theorem.
- Compactness_theorem wikiPageWikiLink Kurt_Gödel.
- Compactness_theorem wikiPageWikiLink Lindstrxc3xb6ms_theorem.
- Compactness_theorem wikiPageWikiLink List_of_Boolean_algebra_topics.
- Compactness_theorem wikiPageWikiLink Löwenheim-Skolem_theorem.
- Compactness_theorem wikiPageWikiLink Löwenheim–Skolem_theorem.
- Compactness_theorem wikiPageWikiLink Mathematical_logic.
- Compactness_theorem wikiPageWikiLink Model_theory.
- Compactness_theorem wikiPageWikiLink Non-standard_analysis.
- Compactness_theorem wikiPageWikiLink Oxford_University_Press.
- Compactness_theorem wikiPageWikiLink Peano_arithmetic.
- Compactness_theorem wikiPageWikiLink Peano_axioms.
- Compactness_theorem wikiPageWikiLink Propositional_calculus.
- Compactness_theorem wikiPageWikiLink Robinsons_principle.
- Compactness_theorem wikiPageWikiLink Stone_space.
- Compactness_theorem wikiPageWikiLink Stones_representation_theorem_for_Boolean_algebras.
- Compactness_theorem wikiPageWikiLink Subset.
- Compactness_theorem wikiPageWikiLink Tychonoffs_theorem.
- Compactness_theorem wikiPageWikiLink Ultrafilter.
- Compactness_theorem wikiPageWikiLink Ultraproduct.
- Compactness_theorem wikiPageWikiLink Upward_Löwenheim–Skolem_theorem.
- Compactness_theorem wikiPageWikiLinkText "(countable) compactness property".
- Compactness_theorem wikiPageWikiLinkText "Compactness theorem".
- Compactness_theorem wikiPageWikiLinkText "compact".
- Compactness_theorem wikiPageWikiLinkText "compactness argument".
- Compactness_theorem wikiPageWikiLinkText "compactness theorem".
- Compactness_theorem wikiPageWikiLinkText "compactness".
- Compactness_theorem hasPhotoCollection Compactness_theorem.
- Compactness_theorem wikiPageUsesTemplate Template:Cite_book.
- Compactness_theorem wikiPageUsesTemplate Template:Cite_journal.
- Compactness_theorem wikiPageUsesTemplate Template:Reflist.
- Compactness_theorem subject Category:Metatheorems.
- Compactness_theorem subject Category:Model_theory.
- Compactness_theorem subject Category:Theorems_in_the_foundations_of_mathematics.
- Compactness_theorem type Theorem.
- Compactness_theorem comment "In mathematical logic, the compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important tool in model theory, as it provides a useful method for constructing models of any set of sentences that is finitely consistent.".
- Compactness_theorem label "Compactness theorem".
- Compactness_theorem sameAs Věta_o_kompaktnosti.
- Compactness_theorem sameAs Kompaktheitssatz_(Logik).
- Compactness_theorem sameAs Kompakteca_teoremo.
- Compactness_theorem sameAs Teorema_de_compacidad.
- Compactness_theorem sameAs Théorème_de_compacité.
- Compactness_theorem sameAs משפט_הקומפקטיות.
- Compactness_theorem sameAs Teorema_di_compattezza_(logica_matematica).
- Compactness_theorem sameAs コンパクト性定理.
- Compactness_theorem sameAs 콤팩트성_정리.
- Compactness_theorem sameAs Twierdzenie_o_zwartości.
- Compactness_theorem sameAs Teorema_ëd_compatëssa.
- Compactness_theorem sameAs Teorema_da_compacidade.
- Compactness_theorem sameAs m.013tmj.
- Compactness_theorem sameAs Теорема_компактности.
- Compactness_theorem sameAs Q1149458.
- Compactness_theorem sameAs Q1149458.
- Compactness_theorem sameAs 紧致性定理.
- Compactness_theorem wasDerivedFrom Compactness_theorem?oldid=618826157.
- Compactness_theorem isPrimaryTopicOf Compactness_theorem.