Definable isomorphism problem

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. The result has been obtained in a joint work with Khadijeh Keshvardoost, Bartek Klin, Joanna Ochremiak and Szymon Torunczyk.

Authors

• Sławomir Lasota.

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