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math.LO2026
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…
math.LO2026
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,…
math.LO2025
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…
math.LO2025
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.