Definable isomorphism problem
Logic in Computer Science
2023-06-22 v3
Abstract
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.
Cite
@article{arxiv.1802.08500,
title = {Definable isomorphism problem},
author = {Khadijeh Keshvardoost and Bartek Klin and Sławomir Lasota and Joanna Ochremiak and Szymon Toruńczyk},
journal= {arXiv preprint arXiv:1802.08500},
year = {2023}
}