Local divisibility and model completeness of a theory of real closed rings
Date
2021-01
Authors
Guier Acosta, Jorge Ignacio
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Abstract
Let T∗ be the theory of lattice-ordered rings convex in von Neumann regular real closed f-rings, without minimal idempotents (non zero) that are divisible-projectable and sc-regular. I introduce a binary relation describing local divisibility. If this relation is added to the language of lattice ordered rings with the radical relation associated to the minimal prime spectrum (cf. [12]), it can be shown the model completeness of T∗.
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Keywords
Model completeness, Real closed ring, Local divisibility
Citation
http://www.logique.jussieu.fr/semsao/index.html