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: http://esolangs.org/wiki/!lyricly%E2%98%ADdemote%E2%98%ADestablish%E2%98%ADcommunism! agrees.
gollark: In the sense of providing a useful diff for humans, not just for... revision tracking.
gollark: UNIMPORTANT QUESTION: how the <:bees:724389994663247974> do you diff human-readable/Markdown text without any convenient linebreaks?
gollark: Well, not as such, but if I wake up *that* early I generally go back to sleep.
gollark: Why would you subject yourself to such suffering?

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