3 papers
math.LO2026
A General Theory of Class Symmetric Systems
Peter Holy, Emma Palmer, Jonathan Schilhan
We develop a general theory for class-sized symmetric systems as a natural extension of symmetric systems with respect to class forcing. In particular, adapting the usual notions o…
math.LO2025
The Ordering Principle and Higher Dependent Choice
Peter Holy, Jonathan Schilhan
We provide, for any regular uncountable cardinal , a new argument for Pincus' result on the consistency of with the higher dependent choice principle $\mathrm{DC}…
math.LO2025
The Ordering Principle and Dependent Choice
Peter Holy, Jonathan Schilhan
We introduce finite support iterations of symmetric systems, and use them to provide a strongly modernized proof of David Pincus' classical result that the axiom of dependent choic…