12 citations · 14 across the 21 of their papers we have counts for
25 papers
Todorcevic's Problem on Rado's Conjecture
Monroe Eskew, Rahman Mohammadpour
In his Mostowski lecture in Wrocław in 2024, Stevo Todorčević asked whether it is consistent that Rado's Conjecture holds at two successive cardinals. We show that it is consistent…
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…
Colors of the Pseudotree
David Chodounský, Monroe Eskew, Thilo Weinert
We investigate big Ramsey degrees of finite substructures of the universal countable homogeneous meet-tree and its binary variant. We prove that structures containing antichains ha…
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…
Chang's Conjectures and Easton collapses
Monroe Eskew, Masahiro Shioya
Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.
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.
Weak saturation properties and side conditions
Monroe Eskew
Towards combining "compactness" and "hugeness" properties at , we investigate the relevance of side-conditions forcing. We reduce the upper bound on the consistency strength o…
Mutually embeddable models of ZFC
Monroe Eskew, Sy-David Friedman, Yair Hayut +1
We investigate systems of transitive models of ZFC which are elementarily embeddable into each other and the influence of definability properties on such systems.
Strong independence and its spectrum
Monroe Eskew, Vera Fischer
For infinite, say is a -maximal independent family if whenever and are pairwise disjoint non-empty in $[\…
Incompatibility of generic hugeness principles
Monroe Eskew
We show that the weakest versions of Foreman's minimal generic hugeness axioms cannot hold simultaneously on adjacent cardinals. Moreover, conventional forcing techniques cannot pr…
Compactness versus hugeness at successor cardinals
Sean Cox, Monroe Eskew
If is regular and , then the existence of a weakly presaturated ideal on implies . This partially answers a question of Foreman and Magidor ab…
Integration with filters
Emanuele Bottazzi, Monroe Eskew
We introduce a notion of integration defined from filters over families of finite sets. This procedure corresponds to determining the average value of functions whose range lies in…
On a strengthening of Jónssonness for
Monroe Eskew
We discuss a system of strengthenings of " is Jónsson" indexed by real numbers, and identify a strongest one. We give a proof of a theorem of Silver and show that there i…
Embeddings into outer models
Monroe Eskew, Sy-David Friedman
We explore the possibilities for elementary embeddings , where and are models of ZFC with the same ordinals, , and has access to large piece…
More rigid ideals
Monroe Eskew
We extend prior results of Cody-Eskew, showing the consistency of GCH with the statement that for all regular cardinals , where is the successor of a regular cardinal,…
Generic large cardinals as axioms
Monroe Eskew
We argue against Foreman's proposal to settle the continuum hypothesis and other classical independent questions via the adoption of generic large cardinal axioms.
Some mutually inconsistent generic large cardinals
Monroe Eskew
Improving a result of Woodin, we identify some classes of individually consistent but mutually inconsistent generic large cardinal axioms.
Coherent forests
Monroe Eskew
A forest is a generalization of a tree, and here we consider the Aronszajn and Suslin properties for forests. We focus on those forests satisfying coherence, a local smallness prop…
Nonregular ideals
Monroe Eskew
Generalizing Keisler's notion of regularity for ultrafilters, Taylor introduced degrees of regularity for ideals and showed that a countably complete nonregular ideal on must…
Local saturation and square everywhere
Monroe Eskew
We show that it is consistent relative to a huge cardinal that for all infinite cardinals , holds and there is a stationary such that $\mathrm{NS}_…
Dense ideals and cardinal arithmetic
Monroe Eskew
From large cardinals we show the consistency of normal, fine, -complete -dense ideals on for successor . We explore the interplay between dense ideals,…
Global Chang's Conjecture and singular cardinals
Monroe Eskew, Yair Hayut
We investigate the possibilities of global versions of Chang's Conjecture that involve singular cardinals. We show some limitations on such principles, and prove rel…
Strongly proper forcing and some problems of Foreman
Sean Cox, Monroe Eskew
We provide solutions to several problems of Foreman about ideals, several of which are closely related to Mitchell's notion of \emph{strongly proper} forcing. We prove: 1) Presatur…
On the consistency of local and global versions of Chang's Conjecture
Monroe Eskew, Yair Hayut
We show that for many pairs of infinite cardinals , is consistent relative to the consistency of a supercompact cardinal. We als…