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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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Is there a noncomputable set which can be described by a probabilistic Turing machine with b...
Construct $A$ as follows. Roll a 6-sided die infinitely many times, giving output $r_1,r_2\dots$.
Now for odd $k$, say $k\in A$ iff $r_k=6$. For even $k$, say $k\in A$ iff $r_k<6$. So $k\in A$ wit …