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dbpedia:First_order_theory	dbpprop:redirect	dbpedia:List_of_first-order_theories .
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dbpedia:List_of_first-order_theories	rdfs:label	"List of first-order theories"@en ;
	dbpprop:abstract	"There are two common ways to specify theories: List or describe a set of sentences in the language L&sigma;, called the axioms of the theory. Give a set of &sigma;-structures, and define a theory to be the set of sentences in L&sigma; holding in all these models. For example, the \"theory of finite fields\" consists of all sentences in the language of fields that are true in all finite fields. A L&sigma; theory may: be consistent: no proof of contradiction exists; be satisfiable: there exists a &sigma;-structure for which the sentences of the theory are all true (by the completeness theorem, satisfiability is equivalent to consistency); be complete: for any statement, either it or its negation is provable; have quantifier elimination; eliminate imaginaries; be finitely axiomatizable; be Decidable: There is an algorithm to decide which statements are provable; be recursively axiomatizable; be Model complete or sub-model complete; be \u03BA-categorical: All models of cardinality \u03BA are isomorphic; be Stable or unstable. be \u03C9-stable (same as totally transcendental for countable theories). be superstable have an atomic model have a prime model have a saturated model"@en ;
	rdfs:comment	"There are two common ways to specify theories: List or describe a set of sentences in the language L&sigma;, called the axioms of the theory. Give a set of &sigma;-structures, and define a theory to be the set of sentences in L&sigma; holding in all these models. For example, the \"theory of finite fields\" consists of all sentences in the language of fields that are true in all finite fields."@en .
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		1965 ,
		"Kochen"@en .
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