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math.LO2026
Universal domination and idealized forcing
Jonathan Schilhan
We introduce the universality property of a definable -ideal on a Polish space, which, on one hand, can serve as a benchmark for the properness of the associated idealized forci…
math.LO2026
Structural Infinite-Exponent Partition Relations and Weak Choice Principles
Lyra A. Gardiner, Jonathan Schilhan
We investigate infinite-exponent partition relations on arbitrary relational structures, with a focus on linear orders and graphs. Any such relation contradicts the Axiom of Choice…
math.LO2026
Towards a theory of symmetric extensions
Asaf Karagila, Jonathan Schilhan
The technique of symmetric extensions is derived from forcing and it is one of the most important tools for studying models without the Axiom of Choice. Despite being incredibly su…