27 citations · 138 across the 42 of their papers we have counts for
6 papers · 2 filters
A new small Dowker space
Assaf Rinot, Roy Shalev, Stevo Todorcevic
It is proved that if there exists a Luzin set, or if either the stick principle or diamond(b) hold, then a strong instance of the guessing principle holds at the f…
Sigma-Prikry forcing III: Down to Aleph_omega
Alejandro Poveda, Assaf Rinot, Dima Sinapova
We prove the consistency of the failure of the singular cardinals hypothesis at together with the reflection of all stationary subsets of . This shows that…
A club guessing toolbox I
Tanmay Inamdar, Assaf Rinot
Club guessing principles were introduced by Shelah as a weakening of Jensen's diamond. Most spectacularly, they were used to prove Shelah's ZFC bound on the power of the first sing…
Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems
Menachem Kojman, Assaf Rinot, Juris Steprans
In this series of papers we advance Ramsey theory of colorings over partitions. In this part, we concentrate on anti-Ramsey relations, or, as they are better known, strong coloring…
Was Ulam right? II: Small width and general ideals
Tanmay Inamdar, Assaf Rinot
We continue our study of Sierpinski-type colourings. In contrast to the prequel paper, we focus here on colourings for ideals stratified by their completeness degree. In particular…
Complicated colorings, revisited
Assaf Rinot, Jing Zhang
In a paper from 1997, Shelah asked whether holds for every inaccessible cardinal . Here, we prove that an affirmative answer follows from . F…