Mutual algebraicity and cellularity
| Autor: | Samuel Braunfeld, Michael C. Laskowski |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: | |
| Popis: | We prove two results intended to streamline proofs about cellularity that pass through mutual algebraicity. First, we show that a countable structure $M$ is cellular if and only if $M$ is $\omega$-categorical and mutually algebraic. Second, if a countable structure $M$ in a finite relational language is mutually algebraic non-cellular, we show it admits an elementary extension adding infinitely many infinite MA-connected components. Towards these results, we introduce MA-presentations of a mutually algebraic structure, in which every atomic formula is mutually algebraic. This allows for an improved quantifier elimination and a decomposition of the structure into independent pieces. We also show this decomposition is largely independent of the MA-presentation chosen. Comment: 18 pages; to appear in Archive for Mathematical Logic |
| Databáze: | OpenAIRE |
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