Deconstructible abstract elementary classes of modules and categoricity
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 di...
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| creator | Šaroch, Jan Trlifaj, Jan |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.2312.02623 |
| format | Article |
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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
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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
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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.</abstract><doi>10.48550/arxiv.2312.02623</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Logic Mathematics - Representation Theory |
| title | Deconstructible abstract elementary classes of modules and categoricity |
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