4 papers · 1 filter
Todorcevic's Problem on Rado's Conjecture
Monroe Eskew, Rahman Mohammadpour
In his Mostowski lecture in WrocÅaw in 2024, Stevo TodorÄeviÄ asked whether it is consistent that Rado's Conjecture holds at two successive cardinals. We show that it is consist…
Comparing forcing approaches to dense ideals
Monroe Eskew
We analyze some posets involved in forcing constructions for dense ideals, showing that the Anonymous Collapse and the Dual Shioya Collapse are equivalent for collapsing a large ca…
Dense ideals
Monroe Eskew, Yair Hayut
In this paper, we obtain the consistency, relative to large cardinals, of the existence of dense ideals on every successor of a regular cardinal simultaneously. Using a consequent…
Saturated ideals from Laver collapses
Monroe Eskew
Addressing a question of Shioya, we show that two-step iterations of the Laver collapse can force saturated ideals and Chang conjectures.