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Corpus ID: 119579070

A Borel-reducibility Counterpart of Shelah's Main Gap Theorem

@article{Hyttinen2016ABC,
title={A Borel-reducibility Counterpart of Shelah's Main Gap Theorem},
author={T. Hyttinen and V. Kulikov and M. Moreno},
journal={arXiv: Logic},
year={2016}
}

We study the Borel-reducibility of isomorphism relations of complete first order theories and show the consistency of the following: For all such theories T and T', if T is classifiable and T' is not, then the isomorphism of models of T' is strictly above the isomorphism of models of T with respect to Borel-reducibility. In fact, we can also ensure that a range of equivalence relations modulo various non-stationary ideals are strictly between those isomorphism relations. The isomorphism… CONTINUE READING