Page "Metalogic" Paragraph 13

In metalogic, ' syntax ' has to do with formal languages or formal systems without regard to any interpretation of them, whereas, ' semantics ' has to do with interpretations of formal languages.

The term ' syntactic ' has a slightly wider scope than ' proof-theoretic ', since it may be applied to properties of formal languages without any deductive systems, as well as to formal systems.

' Semantic ' is synonymous with ' model-theoretic '.