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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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Does finite mathematics need the axiom of infinity?

Doesn't "there is no largest prime" implicitly assume the existence of the natural numbers?
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4 votes

Textbook recommendations for undergraduate proof-writing class

A "book" that satisfies all of your criteria is a set of notes from the Journal of Inquiry Based Mathematics called "Introduction to Proof" by Ron Taylor. linky The chapters are Symbolic Logic Pr …