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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.
3
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Conjecture of a subset of Wang tile which might be decidable
If you're interested in restriction of the domino problem to tile sets with some determinism properties, you might also be interested in this result about 4-way deterministic tile sets.