UNIFORM DEFINABILITY OF INTEGERS IN REDUCED INDECOMPOSABLE POLYNOMIAL RINGS
| Autor: | Marco Barone, Nicolás Caro, Eudes Naziazeno |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Polynomial Logic Polynomial ring 010102 general mathematics Zero (complex analysis) 0102 computer and information sciences Type (model theory) Subring 01 natural sciences Prime (order theory) Philosophy 010201 computation theory & mathematics 0101 mathematics Indecomposable module Commutative property Mathematics |
| Zdroj: | The Journal of Symbolic Logic. 85:1376-1402 |
| ISSN: | 1943-5886 0022-4812 |
| DOI: | 10.1017/jsl.2020.50 |
| Popis: | We prove first-order definability of the prime subring inside polynomial rings, whose coefficient rings are (commutative unital) reduced and indecomposable. This is achieved by means of a uniform formula in the language of rings with signature $(0,1,+,\cdot )$. In the characteristic zero case, the claim implies that the full theory is undecidable, for rings of the referred type. This extends a series of results by Raphael Robinson, holding for certain polynomial integral domains, to a more general class. |
| Databáze: | OpenAIRE |
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