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: Windows is *actually* to be subject to a vast number of bees.
gollark: https://news.ycombinator.com/item?id=26273502
gollark: Apparently Zig is to support using this as a compile target.
gollark: It's very cool and yet horribly accursed.
gollark: Which reminds me, I should put trigonometric functions in!

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