74 citations · 433 across the 68 of their papers we have counts for
5 papers · 2 filters
Chain Conditions and the Axiom of Choice
Ilijas Farah, Jeffrey Marshall-Milne
Within the framework of Zermelo-Fraenkel set theory without the Axiom of Choice, we establish equivalents to the assertion "the union of a countable collection of finite sets is co…
Trivial Isomorphisms between Reduced Products
Ben De Bondt, Ilijas Farah, Alessandro Vignati
We introduce a general method for showing under weak forcing axioms that reduced products of countable models of a theory have as few automorphisms as possible. We show that su…
Quantifier elimination in II factors
Ilijas Farah
No type II tracial von Neumann algebra has theory that admits quantifier elimination.
Hilbert Spaces Without Countable AC
Bruce Blackadar, Ilijas Farah, Asaf Karagila
This article examines Hilbert spaces constructed from sets whose existence is incompatible with the Countable Axiom of Choice (CC). Our point of view is twofold: (1) We examine wha…
Preservation of elementarity by tensor products of tracial von Neumann algebras
Ilijas Farah, Saeed Ghasemi
Tensoring with type I algebras preserves elementary equivalence in the category of tracial von Neumann algebras. The proof involves a novel and general Feferman--Vaught-type theore…