7 papers
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…
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…
The Axiom of Double Complement and its opposites
Hanul Jeon, James E. Hanson
Powell introduced the Axiom of Double Complement () to give his double-negation interpretation of into . However, the consistency,…
Set theory, logic, and homeomorphism groups of manifolds
James E. Hanson, Thomas Koberda, J. de la Nuez González +1
We investigate the relationship between axiomatic set theory and the first-order theory of homeomorphism groups of manifolds in the language of group theory, concentrating on first…
Indiscernible extraction at small large cardinals from a higher-arity stability notion
James E. Hanson
We introduce a higher-arity stability notion defined in terms of -splitting, a higher-arity generalization of splitting. We show that theories with bounded -splitting have im…
Uniqueness of constructible models in continuous logic
James E. Hanson
We show that constructible models of arbitrary complete continuous first-order theories are unique up to isomorphism.