Eilon Bilinsky
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View article: On ultrafilters in ZF models and indecomposable ultrafilters
On ultrafilters in ZF models and indecomposable ultrafilters Open
We use indecomposable ultrafilters to answer some questions from Hayut and Karagila (in Comments Math Univ Carolin 60(2):285–298, 2019). It is shown that the bound on the strength of Usuba (in A note on uniform ultrafilters in choiceless c…
View article: On ultrafilters in ZF models and indecomposable ultrafilters
On ultrafilters in ZF models and indecomposable ultrafilters Open
We use indecomposable ultrafilters to answer some questions of Hayut, Karagila paper "Spectra of uniformity". It is shown that the bound on the strength by T. Usuba "A note on uniform ultrafilters in choiceless context" is optimal.
View article: The Spectra of transitive models
The Spectra of transitive models Open
In this paper we study the spectrum of heights of transitive models of theories extending $V = L[A]$, under various definitions. In particular, we investigate the consistency strength of making those spectra as simple as possible.
View article: On uncountable strongly concentrated sets of reals
On uncountable strongly concentrated sets of reals Open
We construct new models of ZF with an uncountable set of reals that has a unique condensation point. This addresses a question of Sierpiński from 1918.
View article: Uncountable set of reals with unique condensation point
Uncountable set of reals with unique condensation point Open
We construct a model of ZF with an uncountable set of real having a unique condensation point. This answers a question by Sierpinski from 1918.