User:IssaRice/Computability and logic/Some important distinctions and equivalences in introductory mathematical logic: Difference between revisions
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* proves logically vs proves in a particular theory | * proves logically vs proves in a particular theory | ||
* <math>\models</math>: when a set of sentences comes before the symbol vs when a structure comes before the symbol | * <math>\models</math>: when a set of sentences comes before the symbol vs when a structure comes before the symbol | ||
* deciding vs recognizing (semi-deciding, computably enumerating) | |||
Revision as of 22:40, 10 February 2019
This page lists some important distinctions in introductory mathematical logic.
- completeness: semantically complete (complete logic; the topic of the completeness theorem) vs negation-complete (complete theory; the topic of the first incompleteness theorem)
- decides: deciding a sentence vs a theory being decidable vs deciding every sentence vs a logic being decidable
- soundness: sound logic (soundness theorem) vs sound theory
- truth in all interpretations (validity) vs truth in the intended interpretation (natural reading, standard interpretation)
- structure vs interpretation vs model
- theory vs axioms
- language vs logic
- proves logically vs proves in a particular theory
- : when a set of sentences comes before the symbol vs when a structure comes before the symbol
- deciding vs recognizing (semi-deciding, computably enumerating)