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Counterexamples to the Monotone Completeness Conjecture
Jananan Arulseelan, James E. Hanson
Combining a modification of the recent counterexample to the quasitrace conjecture with model-theoretic reductions due to the first author, we exhibit a counterexample to the monot…
Model theory of quasitracial -algebras and the absoluteness of monotone completeness
Jananan Arulseelan
We examine various applications of logic to -algebras, particularly the monotone completeness conjecture. We develop a model theory for -algebras equi…
Revisiting the Transfinite Christensen-Pedersen Argument
Jananan Arulseelan
Christensen and Pedersen proved that every properly infinite -algebra is monotone sequentially complete, and Saitô and Wright developed a transfinite form of their d…
Every -Algebra is Normal
Jananan Arulseelan, James E. Hanson
Using set-theoretic methods, we prove that every -algebra is normal, resolving a question of Wright that has stood open for 46 years. This was previously known in th…
Pointwise Mean Value Theorems in Constructive Mathematics
Jananan Arulseelan, James E. Hanson
We answer some questions regarding the mean value theorem and related results in constructive mathematics. The answers to these questions reveal interesting properties of the Mean…
A Note on Pseudofinite W*-Probability Spaces
Jananan Arulseelan
We introduce pseudofinite W*-probability spaces. These are W*-probability spaces that are elementarily equivalent to Ocneanu ultraproducts of finite-dimensional von Neumann algebra…