Factorial relative commutants and the generalized Jung property for II1 factors

The findings reported in this paper aim to garner the interest of both model theorists and operator algebraists alike. Using a novel blend theoretic algebraic methods, we show that family II 1 factors elementarily equivalent hyperfinite factor R all admit embeddings into U with factorial relative commutant. This answers long standing question Popa for an uncountable factors. We introduce notion generalized Jung factor: M which any two its ultrapower are by automorphism . As application result above, is unique -embeddable factor. concept building von Neumann algebras games recent refutation Connes embedding problem, also there exists does not embed Moreover, find uncountably many non type algebras. study space modulo automorphic equivalence N equip it natural topometric structure, yielding cardinality results certain cases. These investigations naturally connected super McDuff property factors: central sequence algebra provide new examples, classification results, assemble present landscape such Finally, prove transfer theorem inducing commutants on several applications.