first-order theory with identity

<logic> A first-order theory with (x)(x=x) as an axiom, and the following axiom schema, [(x=y) => (A =>A')]^c, when B^c is an arbitrary closure of B, and when A' differs from A only in that y may replace any free occurrence of x in A so long as y is free wherever it replaces x (y need not replace every occurrence of x in A).

See identity, predicate logic with identity

[Glossary of First-Order Logic]

<2001-03-16>

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Nearby terms: first-order logic « first-order predicate logic « first-order theory « first-order theory with identity » five ways » fix » flourishing