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forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
2
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Subsystems of Peano arithmetic and incompleteness theorem
This answers to this question may be of use - Can any formal system prove its own consistency?
In short, it states that $PA$ is too strong to prove its own consistency, Presburger arithmetic (see Nee …
4
votes
Logic in mathematics and philosophy
[I would like to vote up David Corfield's answer - but don't yet have the reputation. Also, having a taught philosophical logic in seminars and now studying mathematical logic, I don't understand what …