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arXiv · 2312.02623

Deconstructible abstract elementary classes of modules and categoricity

Jan Šaroch·Jan Trlifaj
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Abstract

We prove a version of Shelah's Categoricity Conjecture for arbitrary deconstructible classes of modules. Moreover, we show that if $\mathcal{A}$ is a deconstructible class of modules that fits in an abstract elementary class $(\mathcal{A},\preceq)$ such that (1) $\mathcal{A}$ is closed under direct summands and (2) $\preceq$ refines direct summands, then $\mathcal{A}$ is closed under arbitrary direct limits. In an Appendix, we prove that the assumption (2) is not needed in some models of ZFC.

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BibTeXRIS

Jan Šaroch, Jan Trlifaj. 2023-12-05. Deconstructible abstract elementary classes of modules and categoricity. https://arxiv.org/abs/2312.02623

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