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- Absoluteness abstract "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 establish relationships between the absoluteness of formulas and their syntactic form. There are two weaker forms of partial absoluteness. If the truth of a formula in each substructure N of a structure M follows from its truth in M, the formula is downward absolute. If the truth of a formula in a structure N implies its truth in each structure M extending N, the formula is upward absolute.Issues of absoluteness are particularly important in set theory and model theory, fields where multiple structures are considered simultaneously. In model theory, several basic results and definitions are motivated by absoluteness. In set theory, the issue of which properties of sets are absolute is well studied. The Shoenfield absoluteness theorem, due to Joseph Shoenfield (1961), establishes the absoluteness of a large class of formulas between a model of set theory and its constructible universe, with important methodological consequences. The absoluteness of large cardinal axioms is also studied, with positive and negative results known.".
- Absoluteness wikiPageID "12374236".
- Absoluteness wikiPageLength "7737".
- Absoluteness wikiPageOutDegree "33".
- Absoluteness wikiPageRevisionID "683691028".
- Absoluteness wikiPageWikiLink Analytical_hierarchy.
- Absoluteness wikiPageWikiLink Axiom_of_choice.
- Absoluteness wikiPageWikiLink Category:Concepts_in_logic.
- Absoluteness wikiPageWikiLink Category:Mathematical_logic.
- Absoluteness wikiPageWikiLink Conservative_extension.
- Absoluteness wikiPageWikiLink Constructible_universe.
- Absoluteness wikiPageWikiLink Diamond_principle.
- Absoluteness wikiPageWikiLink Elementarily_equivalent.
- Absoluteness wikiPageWikiLink Elementary_equivalence.
- Absoluteness wikiPageWikiLink Elementary_substructure.
- Absoluteness wikiPageWikiLink Forcing_(mathematics).
- Absoluteness wikiPageWikiLink Formula_(mathematical_logic).
- Absoluteness wikiPageWikiLink Kenneth_Kunen.
- Absoluteness wikiPageWikiLink Large_cardinal.
- Absoluteness wikiPageWikiLink Large_cardinal_axiom.
- Absoluteness wikiPageWikiLink Löwenheim-Skolem_theorem.
- Absoluteness wikiPageWikiLink Löwenheim–Skolem_theorem.
- Absoluteness wikiPageWikiLink Mathematical_logic.
- Absoluteness wikiPageWikiLink Measurable_cardinal.
- Absoluteness wikiPageWikiLink Model_complete.
- Absoluteness wikiPageWikiLink Model_complete_theory.
- Absoluteness wikiPageWikiLink Model_theory.
- Absoluteness wikiPageWikiLink P_=_NP_problem.
- Absoluteness wikiPageWikiLink P_versus_NP_problem.
- Absoluteness wikiPageWikiLink Peano_arithmetic.
- Absoluteness wikiPageWikiLink Peano_axioms.
- Absoluteness wikiPageWikiLink Riemann_hypothesis.
- Absoluteness wikiPageWikiLink Set_theory.
- Absoluteness wikiPageWikiLink Skolems_paradox.
- Absoluteness wikiPageWikiLink Structure_(mathematical_logic).
- Absoluteness wikiPageWikiLink Substructure.
- Absoluteness wikiPageWikiLink Thomas_Jech.
- Absoluteness wikiPageWikiLink Transitive_set.
- Absoluteness wikiPageWikiLink Truth_value.
- Absoluteness wikiPageWikiLink Well-formed_formula.
- Absoluteness wikiPageWikiLinkText "Absoluteness".
- Absoluteness wikiPageWikiLinkText "Absoluteness#Shoenfield's absoluteness theorem".
- Absoluteness wikiPageWikiLinkText "absolute".
- Absoluteness wikiPageWikiLinkText "absoluteness".
- Absoluteness hasPhotoCollection Absoluteness.
- Absoluteness subject Category:Concepts_in_logic.
- Absoluteness subject Category:Mathematical_logic.
- Absoluteness type Concept.
- Absoluteness type Field.
- Absoluteness comment "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 establish relationships between the absoluteness of formulas and their syntactic form. There are two weaker forms of partial absoluteness. If the truth of a formula in each substructure N of a structure M follows from its truth in M, the formula is downward absolute.".
- Absoluteness label "Absoluteness".
- Absoluteness sameAs m.02w1s8v.
- Absoluteness sameAs Q4669873.
- Absoluteness sameAs Q4669873.
- Absoluteness wasDerivedFrom Absoluteness?oldid=683691028.
- Absoluteness isPrimaryTopicOf Absoluteness.