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On ‐complete equivalence relations on the generalized Baire space
Mathematical Logic Quarterly 61 (1-2):66-81 (2015)
Abstract
Working with uncountable structures of fixed cardinality, we investigate the complexity of certain equivalence relations and show that if, then many of them are ‐complete, in particular the isomorphism relation of dense linear orders. Then we show that it is undecidable in whether or not the isomorphism relation of a certain well behaved theory (stable, NDOP, NOTOP) is ‐complete (it is, if, but can be forced not to be).My notes
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Citations of this work
The isomorphism relation of theories with S-DOP in the generalised Baire spaces.Miguel Moreno - 2022 - Annals of Pure and Applied Logic 173 (2):103044.
On the reducibility of isomorphism relations.Tapani Hyttinen & Miguel Moreno - 2017 - Mathematical Logic Quarterly 63 (3-4):175-192.
The complexity of the embeddability relation between torsion-free Abelian groups of uncountable size.Filippo Calderoni - 2018 - Journal of Symbolic Logic 83 (2):703-716.
Reducibility of Equivalence Relations Arising from Nonstationary Ideals under Large Cardinal Assumptions.David Asperó, Tapani Hyttinen, Vadim Kulikov & Miguel Moreno - 2019 - Notre Dame Journal of Formal Logic 60 (4):665-682.
References found in this work
A borel reducibility theory for classes of countable structures.Harvey Friedman & Lee Stanley - 1989 - Journal of Symbolic Logic 54 (3):894-914.
Constructing strongly equivalent nonisomorphic models for unstable theories.Tapani Hyttinen & Heikki Tuuri - 1991 - Annals of Pure and Applied Logic 52 (3):203-248.
Trees and -subsets of ω1ω1.Alan Mekler & Jouko Väänänen - 1993 - Journal of Symbolic Logic 58 (3):1052-1070.
Trees and Π 1 1 -Subsets of ω1 ω 1.Alan Mekler & Jouko Vaananen - 1993 - Journal of Symbolic Logic 58 (3):1052 - 1070.
The descriptive set-theoretical complexity of the embeddability relation on models of large size.Luca Motto Ros - 2013 - Annals of Pure and Applied Logic 164 (12):1454-1492.
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