Definable isomorphism problem

  title={Definable isomorphism problem},
  author={Khadijeh Keshvardoost and Bartek Klin and Slawomir Lasota and Joanna Ochremiak and Szymon Toruńczyk},
  journal={Log. Methods Comput. Sci.},
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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