2016/02/01 by Tapani Hyttinen, Hyttinen, Tapani, Vadim Kulikov +3
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1602.00605
openalex publication_date 2016/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 relations are considered on models of some fixed uncountable cardinality obeying certain restrictions.