Year: 2019
Type: article
Abstract: Answering some of the main questions from [L. Motto Ros, The descriptive set-theoretical complexity of the embeddability relation on models of large size, Ann. Pure Appl. Logic 164(12) (2013) 1454–1492], we show that whenever [Formula: see text] is a cardinal satisfying [Formula: see text], then the embeddability relation between [Formula: see text]-sized structures is strongly invariantly universal, and hence complete for ([Formula: see text]-)analytic quasi-orders. We also prove that in the above result we can further restrict our attention to various natural classes of structures, including (generalized) trees, graphs, or groups. This fully generalizes to the uncountable case the main results of [A. Louveau and C. Rosendal, Complete analytic equivalence relations, Trans. Amer. Math. Soc. 357(12) (2005) 4839–4866; S.-D. Friedman and L. Motto Ros, Analytic equivalence relations and bi-embeddability, J. Symbolic Logic 76(1) (2011) 243–266; J. Williams, Universal countable Borel quasi-orders, J. Symbolic Logic 79(3) (2014) 928–954; F. Calderoni and L. Motto Ros, Universality of group embeddability, Proc. Amer. Math. Soc. 146 (2018) 1765–1780].
Source: Journal of Mathematical Logic
Authors: Filippo Calderoni, Heike Mildenberger, Luca Motto Ros
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2953812076