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first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.

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How to show that the set of universal sentences with infinite models is a decidable set?

I was looking for an example for a a non- complete set of formulas (not finite) that might be decidable and I found the following statement: Given a recursive language $L$ the set $\{ \phi \ | \ \phi …