Elementary theory

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In mathematical logic, an elementary theory is a theory that involves axioms using only finitary first-order logic, without reference to set theory or using any axioms that have consistency strength equal to set theory.

Saying that a theory is elementary is a weaker condition than saying it is algebraic.

Examples

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Examples of elementary theories include:

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References

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  • Mac Lane and Moerdijk, Sheaves in Geometry and Logic: A First Introduction to Topos Theory, page 4.