Difference between revisions of "User:IssaRice/Computability and logic/Expresses versus captures"

From Machinelearning
Jump to: navigation, search
Line 14: Line 14:
 
| Goldrei ||
 
| Goldrei ||
 
|-
 
|-
| Boolos, Burgess, Jeffrey || ||
+
| Boolos, Burgess, Jeffrey || arithmetically defines ||
 
|-
 
|-
 
| Wikipedia || ||
 
| Wikipedia || ||
 
|}
 
|}

Revision as of 01:09, 7 February 2019

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