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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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Provability of termination. Whats wrong with my reasoning?
Let A be a pair (i, x)
$H(A)$ <=> program i halts on input x
$P(A)$ <=> (there exists a proof for $H(A)$) $\vee$ (there exists a proof for $\neg H(A)$)
Assume $\forall A: P(A)$ then we can solve th …