Hereditary undecidability of some theories of finite structures

Journal of Symbolic Logic 59 (4):1254-1262 (1994)
Abstract
Using a result of Gurevich and Lewis on the word problem for finite semigroups, we give short proofs that the following theories are hereditarily undecidable: (1) finite graphs of vertex-degree at most 3; (2) finite nonvoid sets with two distinguished permutations; (3) finite-dimensional vector spaces over a finite field with two distinguished endomorphisms
Keywords Undecidable theory   interpretable   finite graphs   word problem
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