2 citations · 2 across the 10 of their papers we have counts for
10 papers
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…
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…
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…
Transcendence degrees over mutually generic extensions
Jonathan Schilhan
Let ,..., be mutually generic over , each adding at least one new real over . We show that the transcendence degree of the reals of $V[G_0, \dots, G_{n-1…
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}_…
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…
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 to denote that there is some for which…
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…
Geometric condition for Dependent Choice
Asaf Karagila, Jonathan Schilhan
We provide a geometric condition which characterises when the Principle of Dependent Choice holds in a Fraenkel--Mostowski--Specker permutation model. This condition is a slight we…
Sequential and distributive forcings without choice
Asaf Karagila, Jonathan Schilhan
In the Zermelo--Fraenkel set theory with the Axiom of Choice a forcing notion is "-distributive" if and only if it is "-sequential". We show that without the Axiom of Choice…