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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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(When) is the range of a bijection $f\in M[G]$ in the ground model $M$?
Let $M$ be a countable transitive model of ZF-P, $\mathbb P$ the set of injections from a countable subset of $\mathbb R$ into $\omega_1$ with $\le=\supseteq$. Let $G$ be a $\mathbb P^M$-generic filte …