Elementary definition

In mathematical logic, an elementary definition is a definition that can be made using only finitary first-order logic, and in particular without reference to set theory or using extensions such as plural quantification. Elementary definitions are of particular interest because they admit a complete proof apparatus while still being expressive enough to support most everyday mathematics (via the addition of elementarily-expressible axioms such as Zermelo–Fraenkel set theory (ZFC)).

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

gollark: `int something`
gollark: ++magic py " ".join(map(lambda x: x[1:], "segmentation fault: laser bee deployment initiated".split(" ")))
gollark: This is way lower latency than the TIO thing.
gollark: ++magic py " ".join(map(lambda x: x[1:], "segmentation fault".split(" ")))
gollark: All <input> element nodes have a files attribute of type FileList on them which allows access to the items in this list. For example, if the HTML includes the following file input:

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