User:IssaRice/Computability and logic/Expresses versus captures

The expresses versus captures distinction is an important one in mathematical logic, but unfortunately the terminology differs wildly between different texts. The following table gives a comparison.

• Expressing is done by a language. There is only one form of expressing; I think this follows from the wikipedia:Law of excluded middle.
• Capturing is done by a theory or by axioms. There are two forms of capturing: strong capture (corresponding to deciding), and weak capture (corresponding to recognizing, or semi-deciding).

Text	"Expresses"	"Captures"
Peter Smith. Godel book	expresses	captures
Leary & Kristiansen	defines	represents
Goldrei
Boolos, Burgess, Jeffrey	arithmetically defines
Wikipedia