Elementary theory

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

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

gollark: What?
gollark: Impossible.
gollark: pM them?
gollark: Or stay there as lon.
gollark: There is some selection bias. Neat things will not reach the AP as often.

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