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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.
8
votes
Textbook recommendations for undergraduate proof-writing class
I have used Velleman's How to Prove It with success.
28
votes
What if Current Foundations of Mathematics are Inconsistent?
I once heard Mike Freedman (the Fields medalist) say he thinks ZFC is probably inconsistent but that the minimal length paradox is so long no-one has found it yet. Once a paradox is found, he said, we …