User:IssaRice/Computability and logic/Some important distinctions and equivalences in introductory mathematical logic: Difference between revisions
(→notes) |
|||
| Line 74: | Line 74: | ||
* <math>\models</math>: when a set of sentences comes before the symbol vs when a structure comes before the symbol: see [[../Models symbol]] | * <math>\models</math>: when a set of sentences comes before the symbol vs when a structure comes before the symbol: see [[../Models symbol]] | ||
* deciding (corresponding to computable ''total'' functions) vs recognizing (semi-deciding, computably enumerating; corresponding to computable ''partial'' functions) | * deciding (corresponding to computable ''total'' functions) vs recognizing (semi-deciding, computably enumerating; corresponding to computable ''partial'' functions) | ||
* algorithm vs function computed by algorithm: see [[../Function versus algorithm]] | * algorithm vs function computed by algorithm: see [[../Function versus algorithm]] | ||
* expresses vs captures (strong capture, weak capture): see [[../Expresses versus captures]] | * expresses vs captures (strong capture, weak capture): see [[../Expresses versus captures]] | ||