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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.
4
votes
Words which are not inverted by any endomorphism
This partial answer just covers the case of $\psi$ non-surjective, i.e. not an automorphism.
Just to set some notation: Define $A=\langle w_1, w_2\rangle=\operatorname{im}(\phi)\leq F_2$. We will show …