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: SpoutServer?

gollark: I reject your mathematical axioms and substitute my own.

gollark: According to a class-η apioformic quality algorithm, we are 128946 quality.

gollark: Heavserver is cool and good™.

gollark: heavserver > heavserver.

References

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

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.