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Preprint Number 1152

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1152. Isaac Goldbring, Bradd Hart, and Henry Towsner
Explicit sentences distinguishing McDuff's II_1 factors

Submission date: 27 January 2017


Recently, Boutonnet, Chifan, and Ioana proved that McDuff's examples of continuum many pairwise non-isomorphic separable II_1 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-Fraïssé 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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Full text arXiv 1701.07928: pdf, ps.

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