Deconstructible abstract elementary classes of modules and categoricity

Autor:	Šaroch, Jan, Trlifaj, Jan
Rok vydání:	2023
Předmět:	Mathematics - Representation Theory Mathematics - Logic 03C95 16E30 (primary) 03C35 16D10 (secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 11 pages; Appendix added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.02623 Zobrazit plný text záznamu View this record from Arxiv