Hyperfinite MV-algebras
| Autor: | L. P. Belluce, A. Di Nola, Giacomo Lenzi |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory Mathematics::Operator Algebras 010102 general mathematics Elementary equivalence MV-algebra 02 engineering and technology 01 natural sciences Decidability decidable theory Mathematics::Logic Product (mathematics) MV-chain 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing 0101 mathematics Hyperfinite set Mathematics |
| Zdroj: | Journal of Pure and Applied Algebra. 217:1208-1223 |
| ISSN: | 0022-4049 |
| DOI: | 10.1016/j.jpaa.2012.10.012 |
| Popis: | In this paper, we will be concerned with Hyperfinite MV-algebras, which are infinite models of the theory of finite MV-algebras. We have three main results. As a first main result, we show that every hyperfinite MV-algebra is elementarily equivalent to a product of finite or hyperfinite MV-chains. As a second main result, we give an explicit, recursive axiomatization of finite or hyperfinite MV-algebras; this implies the decidability of the theory of all finite MV-algebras. As a third main result, we show that if A is a hyperfinite MV-algebra, then A / R a d ( A ) is infinite. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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