Jonathan Schilhan

collaborators

7 papers

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…

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 $I^º$ , a new argument for Pincus' result on the consistency of $ZF$ with the higher dependent choice principle $\mathrm{DC}…

math.LO2025

Upwards homogeneity in iterated symmetric extensions

Calliope Ryan-Smith, Jonathan Schilhan, Yujun Wei

It is sometimes desirable in choiceless constructions of set theory that one iteratively extends some ground model without adding new sets of ordinals after the first extension. Pu…

math.LO2025

Intermediate models and Kinna--Wagner Principles

Asaf Karagila, Jonathan Schilhan

Kinna--Wagner Principles state that every set can be mapped into some fixed iterated power set of an ordinal, and we write $KWP$ to denote that there is some $I^\pm$ for whic…