About: O-minimal theory

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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 M) is a finite union of intervals and points.

Attributes	Values
rdf:type	organisation
rdfs:label	O-minimal theory (en)
rdfs:comment	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 M) is a finite union of intervals and points. (en)
dcterms:subject	Real algebraic geometry Topology Mathematical logic Model theory
Wikipage page ID	30865852 (xsd:integer)
Wikipage revision ID	1120471633 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Quantifier elimination Model theory Semialgebraic set Annals of Mathematics Real algebraic geometry Definable set Analytic function Mathematical logic Pfaffian function Theory Complete theory Stratification (mathematics) Structure (mathematical logic) Total order Topology Exponential function Journal of the American Mathematical Society Hassler Whitney Interval (mathematics) Jean-Louis Verdier Mathematical logic Model theory Theory (mathematical logic) Real algebraic geometry Boolean algebra (structure) Bulletin of the AMS C-minimal theory Real closed field Real number Union (set theory) Wilkie's theorem Strongly minimal theory Łojasiewicz inequality Tame topology Weakly o-minimal structure Transactions of the American Mathematical Society Springer-Verlag
Link from a Wikipage to an external page	http://www.logique.jussieu.fr/modnet/Publications/Preprint%20server/ http://www.maths.manchester.ac.uk/raag/ https://www.ams.org/bull/2000-37-03/S0273-0979-00-00866-1/S0273-0979-00-00866-1.pdf https://www.ams.org/jams/1996-9-04/S0894-0347-96-00216-0/S0894-0347-96-00216-0.pdf https://www.ams.org/journals/tran/1986-295-02/S0002-9947-1986-0833697-X/S0002-9947-1986-0833697-X.pdf
sameAs	O-minimal theory O-minimal theory O-minimal theory O-minimal theory
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Reflist dbt:Mathematical_logic
has abstract	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 M) is a finite union of intervals and points. O-minimality can be regarded as a weak form of quantifier elimination. A structure M is o-minimal if and only if every formula with one free variable and parameters in M is equivalent to a quantifier-free formula involving only the ordering, also with parameters in M. This is analogous to the minimal structures, which are exactly the analogous property down to equality. A theory T is an o-minimal theory if every model of T is o-minimal. It is known that the complete theory T of an o-minimal structure is an o-minimal theory. This result is remarkable because, in contrast, the complete theory of a minimal structure need not be a strongly minimal theory, that is, there may be an elementarily equivalent structure which is not minimal. (en)
gold:hypernym	Union
prov:wasDerivedFrom	wikipedia-en:O-minimal_theory?oldid=1120471633&ns=0
page length (characters) of wiki page	10771 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:O-minimal_theory
is Link from a Wikipage to another Wikipage of	NIP (model theory) Jonathan Pila Umberto Zannier List of mathematical logic topics O-minimal Mathematical logic Hardy field Cyclic order André–Oort conjecture C-minimal theory Strongly minimal theory O-minimal structure O-minimality
is Wikipage redirect of	O-minimal O-minimal structure O-minimality
is foaf:primaryTopic of	wikipedia-en:O-minimal_theory

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