Quantifier elimination in C*-algebras

2015/02/02 by Christopher J. Eagle, Eagle, Christopher J., Ilijas Farah +5 · 1 citation
Computer Science · Mathematics · #03C10 #03C65 #03C90 #46L05 #46L89 #46M07 #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Logic (math.LO) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1502.00573

openalex publication_date 2015/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The only C*-algebras that admit elimination of quantifiers in continuous logic are ℂ, ℂ², C(Cantor space) and M₂(ℂ). We also prove that the theory of C*-algebras does not have model companion and show that the theory of M_n(\mathcal O_n+1) is not ∀∃-axiomatizable for any n≥ 2.

Citations

• Logic and operator algebras
• Invariant means and finite representation theory of C*-algebras

Cited by

• Expressive power of infinitary [0, 1]-valued logics

Related

• Concrete Barriers to Quantifier Elimination in Finite-Dimensional C*-algebras
• Model theory of C^*-algebras
• On elimination of quantifiers in some non-classical mathematical theories
• Model theory of a non-degenerate representation of a unital C*-algebra
• Algebraic Logic, I Quantifier Theories and Completeness Theorems