About: Positive set theory

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In mathematical logic, positive set theory is the name for a class of alternative set theories in which the axiom of comprehension holds for at least the positive formulas (the smallest class of formulas containing atomic membership and equality formulas and closed under conjunction, disjunction, existential and universal quantification).

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rdfs:label	Positive set theory (en) 正集合论 (zh)
rdfs:comment	在數理邏輯中，一種作為替代的集合論稱為一種正集合論（Positive set theory），如果分離公理 * " exists" 對正公式成立。注意正集合論是以上這一系列集合論的總體，而不僅是「一個」集合理論。 (zh) In mathematical logic, positive set theory is the name for a class of alternative set theories in which the axiom of comprehension holds for at least the positive formulas (the smallest class of formulas containing atomic membership and equality formulas and closed under conjunction, disjunction, existential and universal quantification). (en)
dcterms:subject	Systems of set theory
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Wikipage revision ID	1087474157 (xsd:integer)
Link from a Wikipage to another Wikipage	New Foundations John von Neumann Von Neumann–Bernays–Gödel set theory Compact spaces Mathematical logic Topology Isaac Malitz Alonzo Church Systems of set theory Weakly compact cardinal ZFC Axiom of extensionality Axiom of infinity Ordinal number Set theory Topological closure Universal set Morse–Kelley set theory Axiom of comprehension W. V. Quine Logical constants dbr:Olivier_Esser
sameAs	Positive set theory Positive set theory Positive set theory Positive set theory Positive set theory
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Reflist dbt:Short_description
has abstract	In mathematical logic, positive set theory is the name for a class of alternative set theories in which the axiom of comprehension holds for at least the positive formulas (the smallest class of formulas containing atomic membership and equality formulas and closed under conjunction, disjunction, existential and universal quantification). Typically, the motivation for these theories is topological: the sets are the classes which are closed under a certain topology. The closure conditions for the various constructions allowed in building positive formulas are readily motivated (and one can further justify the use of universal quantifiers bounded in sets to get generalized positive comprehension): the justification of the existential quantifier seems to require that the topology be compact. (en) 在數理邏輯中，一種作為替代的集合論稱為一種正集合論（Positive set theory），如果分離公理 * " exists" 對正公式成立。注意正集合論是以上這一系列集合論的總體，而不僅是「一個」集合理論。 (zh)
prov:wasDerivedFrom	wikipedia-en:Positive_set_theory?oldid=1087474157&ns=0
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foaf:isPrimaryTopicOf	wikipedia-en:Positive_set_theory
is Link from a Wikipage to another Wikipage of	List of first-order theories New Foundations List of mathematical logic topics List of set theory topics Axiom schema of specification Isaac Malitz Alternative set theory Positive formula Universal set
is Wikipage redirect of	Positive formula
is foaf:primaryTopic of	wikipedia-en:Positive_set_theory

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