On unsuperstable theories in GDST

Miguel Fernando Moreno Wandurraga

doi:10.1017/jsl.2023.82

On unsuperstable theories in GDST

Miguel Fernando Moreno Wandurraga (Corresponding author)

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We study the $k$-Borel-reducibility of isomorphism relations of complete first-order theories by using coloured trees. Under some cardinality assumptions, we show the following: For all theories T and T’, if T is classifiable and T’ is unsuperstable, then the isomorphism of models of T’ is strictly above the isomorphism of models of T with respect to $k$-Borel-reducibility.

Original language	English
Pages (from-to)	1720-1746
Number of pages	27
Journal	The Journal of Symbolic Logic
Volume	89
Issue number	4
DOIs	https://doi.org/10.1017/jsl.2023.82
Publication status	Published - 2024

Austrian Fields of Science 2012

101013 Mathematical logic

Keywords

Ehrenfeucht-Mostowski models
classification theory
coloured trees
generalized descriptive set theory
isomorphism

Access to Document

10.1017/jsl.2023.82

Cite this

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title = "On unsuperstable theories in GDST",

abstract = "We study the \$k\$-Borel-reducibility of isomorphism relations of complete first-order theories by using coloured trees. Under some cardinality assumptions, we show the following: For all theories T and T{\textquoteright}, if T is classifiable and T{\textquoteright} is unsuperstable, then the isomorphism of models of T{\textquoteright} is strictly above the isomorphism of models of T with respect to \$k\$-Borel-reducibility.",

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KW - generalized descriptive set theory

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