Explicit sentences distinguishing McDuff's II₁ factors

2017/01/27 by Isaac Goldbring, Goldbring, Isaac, Bradd Hart +3
Computer Science · Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1701.07928

openalex publication_date 2017/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, Boutonnet, Chifan, and Ioana proved that McDuff's examples of continuum many pairwise non-isomorphic separable II₁ factors are in fact pairwise non-elementarily equivalent. Their proof proceeded by showing that any ultrapowers of any two distinct McDuff examples are not isomorphic. In a paper by the first two authors of this paper, Ehrenfeucht-Fraïsse games were used to find an upper bound on the quantifier complexity of sentences distinguishing the McDuff examples, leaving it as an open question to find concrete sentences distinguishing the McDuff factors. In this paper, we answer this question by providing such concrete sentences.

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