# Definable isomorphism problem

@article{Keshvardoost2019DefinableIP, title={Definable isomorphism problem}, author={Khadijeh Keshvardoost and Bartek Klin and Slawomir Lasota and Joanna Ochremiak and Szymon Toruńczyk}, journal={Log. Methods Comput. Sci.}, year={2019}, volume={15} }

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.

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