Jonathan Schilhan

activity

20192026

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5 papers · 1 filter

math.LO2026

Hagendorf Orders

Jonathan Schilhan, Thilo Weinert

Call a linear order type $φ$ Hagendorf if it shares two properties with additively indecomposable ordinal numbers without being one itself: $φ$ is strictly indecomposable to the ri…

math.LO2026

Infinite-Exponent Partition Relations on Higher Analogues of the Real Line

Lyra A. Gardiner, Jonathan Schilhan, Thilo Weinert

We present a number of results concerning infinite-exponent partition relations on linear orders of the form $⟨^{α} 2, <_{lex} ⟩$ for $α$ an ordinal, generalising…

math.LO2023

Wetzel families and the continuum

Jonathan Schilhan, Thilo Weinert

We provide answers to a question brought up by Erdős about the construction of Wetzel families in the absence of the continuum hypothesis - a Wetzel family is a family $\mathcal{F}…

math.LO2020

Tree forcing and definable maximal independent sets in hypergraphs

Jonathan Schilhan

We show that after forcing with a countable support iteration or a finite product of Sacks or splitting forcing over $L$ , every analytic hypergraph on a Polish space admits a $\mat…

math.LO2019

Coanalytic Ultrafilter Bases

Jonathan Schilhan

We study the definability of ultrafilter bases on $ω$ in the sense of descriptive set theory. As a main result we show that there is no coanalytic base for a Ramsey ultrafilter, wh…