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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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Other ways to define naturals

As I recall from reading and classes in mathematical logic, the natural numbers are "defined"--postulated might be a better word--more or less as follows: A.) There is a set $N$; B.) $N$ has a "pref …
drbobmeister's user avatar