First-order theory Created 2026-09-24 Updated 2026-10-14
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A first-order theory is a set of sentences in one first-order language. Depending on convention, the term may instead mean its deductive closure.
This is a theory formulated in first-order logic.
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Theory (mathematical logic) 2026-10-14
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A theory is a set of sentences in a formal language, sometimes understood to be closed under deduction. A first-order theory uses a first-order language; consistency and completeness are separate properties of a theory.
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