Model completeness and quantifier elimination for (ordered) central simple algebras with involution

2025/03/04 by Astier, Vincent
#03C10 (Primary) #13J30 #16K20 (Secondary) #16W10 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2503.03028

Abstract

We show that the theories of some (ordered) central simple algebras with involution over real closed fields are model-complete or admit quantifier elimination, and characterize positive cones in terms of morphisms into models of some of these theories.

Related

• Model completions for universal classes of algebras: necessary and sufficient conditions
• Model theory of fields with free operators in positive characteristic
• Affinization and quantifier-elimination
• Quantifier elimination in C*-algebras
• The theory of tracial von Neumann algebras does not have a model companion