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Theory (mathematical logic)

In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first understood from context, after which an element of a deductively closed theory is then called a theorem of the theory. In many deductive systems there is usually a subset that is called "the set of axioms" of the theory , in which case the deductive system is also called an "axiomatic system". By definition, every axiom is automatically a theorem. A first-order theory is a set of first-order sentences (theorems) recursively obtained by the inference rules of the system applied to the set of axioms.

"Logical theory" redirects here. For John Dewey's "Studies in Logical Theory", see John Dewey.

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(1997). A shorter model theory. Cambridge University Press. ISBN 0-521-58713-1.

Hodges, Wilfrid

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Examples[edit]

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