Definable isomorphism problem
Khadijeh Keshvardoost, Bartek Klin, Sławomir Lasota, Joanna Ochremiak, Szymon Toruńczyk · Logical Methods in Computer Science · 2019
We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying structure of atoms, we prove decidability of the problem. The core result is parameter-elimination: existence of an isomorphism definable with parameters implies existence of an isomorphism definable without parameters.