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Trakhtenbrot's Theorem in Coq
[chapter]
2020
Lecture Notes in Computer Science
We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory. Employing synthetic accounts of enumerability and decidability, we give a full classification of FSAT depending on the first-order signature of non-logical symbols. On the one hand, our development focuses on Trakhtenbrot's theorem, stating that FSAT is undecidable as soon as the signature contains an at least binary relation symbol. Our proof proceeds by a many-one reduction chain starting
doi:10.1007/978-3-030-51054-1_5
fatcat:utx3rwhqr5bcdnwf5bnuzvzdyi