# User:IssaRice/Computability and logic/Some important distinctions and equivalences in introductory mathematical logic

From Machinelearning

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
- : when a set of sentences comes before the symbol vs when a structure comes before the symbol