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: It's different but exists.
gollark: That's pretty cool, though.
gollark: It seems to be piephon.
gollark: It's basically a reflection of the fact that Java is bad and Kotlin less bad.
gollark: Should it not be a node tree, anyway?

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