Jonathan Schilhan

collaborators

3 papers

math.LO2025

Transcendence degrees over mutually generic extensions

Jonathan Schilhan

Let $G_{0}$ ,..., $G_{n - 1}$ be mutually generic over $V$ , each $G_{i}$ adding at least one new real over $V$ . We show that the transcendence degree of the reals of $V[G_0, \dots, G_{n-1…

math.LO2025

The Ordering Principle and Higher Dependent Choice

Peter Holy, Jonathan Schilhan

We provide, for any regular uncountable cardinal $κ$ , a new argument for Pincus' result on the consistency of $ZF$ 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…