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math.LO2026
Short proof that Vopěnka's Principle is symmetrically stable
Asaf Karagila
We show that Vopěnka's Principle is stable under symmetric extensions. Recently, de Groot and Woloszyn [1] proved this fact. We found the proof of this theorem unnecessarily compli…
math.LO2026
Comments on Choiceless Chain Conditions
Constance Bromham, Asaf Karagila
In [10] it was suggested that the countable chain condition should be defined in the absence of choice as "every predense set contains a countable predense subset". During his tuto…
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…