6 citations · 16 across the 19 of their papers we have counts for
26 papers
How robustly can you predict the future?
Sean Cox, Matthew Elpers
Hardin and Taylor \cite{MR2384262} proved that any function on the reals -- even a nowhere continuous one -- can be correctly predicted, based solely on its past behavior, at almos…
Sparse analytic systems
Brent Cody, Sean Cox, Kayla Lee
Erdős \cite{MR168482} proved that the Continuum Hypothesis (CH) is equivalent to the existence of an uncountable family of (real or complex) analytic functions, such…
The Diagonal Strong Reflection Principle and its fragments
Sean Cox, Gunter Fuchs
A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated to arbitrary forcing classes. The relationships between the r…
Salce's problem on cotorsion pairs is undecidable
Sean Cox
Salce \cite{MR565595} introduced the notion of a \emph{cotorsion pair} of classes of abelian groups, and asked whether every such pair is \emph{complete} (i.e., has enough injectiv…
Maximum deconstructibility in module categories
Sean Cox
We prove that Vopěnka's Principle implies that for every class of modules over any ring, the class of \textbf{-Gorenstein Projective modul…
Forcing axioms and the complexity of non-stationary ideals
Sean Cox, Philipp Lücke
We study the influence of strong forcing axioms on the complexity of the non-stationary ideal on and its restrictions to certain cofinalities. Our main result shows that the…
Filtration Games and Potentially Projective Modules
Sean D. Cox
The notion of a \textbf{-filtered} object, where is some (typically small) collection of objects in a Grothendieck category, has become ubiq…
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…
The Löwenheim-Skolem-Tarski property of Stationary Logic
Sean Cox
Fuchino-Maschio-Sakai~\cite{FuchinoEtAl_DRP_LST} proved that the Löwenheim-Skolem-Tarski (LST) property of Stationary Logic is equivalent to the Diagonal Reflection Principle on in…
Adjoining only the things you want: a survey of Strong Chang's Conjecture and related topics
Sean Cox
We survey some old and new results on strong variants of Chang's Conjecture and related topics.
Martin's Maximum and the Diagonal Reflection Principle
Sean Cox, Hiroshi Sakai
We prove that Martin's Maximum does not imply the Diagonal Reflection Principle for stationary subsets of .
A variant of Shelah's characterization of Strong Chang's Conjecture
Sean Cox, Hiroshi Sakai
Shelah considered a certain version of Strong Chang's Conjecture, which we denote , and proved that it is equivalent to several statements, including the a…
Club Chang's Conjecture
Sean Cox, Saharon Shelah
Chang's Conjecture (CC) asserts that for every , there exists an that is closed under such that and . By classic results of…
Forcing axioms, approachability, and stationary set reflection
Sean D. Cox
We prove a variety of theorems about stationary set reflection and concepts related to internal approachability. We prove that an implication of Fuchino-Usuba relating stationary r…
On the universality of the nonstationary ideal
Sean Cox
Burke \cite{MR1472122} proved that the generalized nonstationary ideal, denoted NS, is universal in the following sense: every normal ideal, and every tower of normal ideals of ina…
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…
Namba forcing, weak approximation, and guessing
Sean Cox, John Krueger
We prove a variation of Easton's lemma for strongly proper forcings, and use it to prove that, unlike the stronger principle , together with $2^ω\le ω…
Lower consistency bounds for mutual stationarity with divergent uncountable cofinalities
Dominik Adolf, Sean Cox, Philip Welch
We prove that the upper bounds for the consistency strength of certain instances of mutual stationarity considered by Liu-Shelah~\cite{MR1469093} are close to optimal. We also cons…
Chang's Conjecture and semiproperness of nonreasonable posets
Sean D. Cox
Let denote the poset which adds a Cohen real then shoots a club through the complement of with countable conditions. We prove that the version o…
Indestructible Guessing Models and the Continuum
Sean Cox, John Krueger
We introduce a stronger version of an -guessing model, which we call an indestructibly -guessing model. The principle IGMP states that there are stationarily many indestr…
Characterizing large cardinals in terms of layered posets
Sean Cox, Philipp Lücke
Given an uncountable regular cardinal , a partial order is -stationarily layered if the collection of regular suborders of of cardinality less than is statio…
Layered posets and Kunen's universal collapse
Sean D. Cox
We develop the theory of layered posets, and use the notion of layering to prove a new iteration theorem (Theorem 6): if is weakly compact then any universal Kunen iteration of…
Quotients of Strongly Proper Forcings and Guessing Models
Sean Cox, John Krueger
We prove that a wide class of strongly proper forcing posets have quotients with strong properties. Specifically, we prove that quotients of forcing posets which have simple univer…
Prevalence of Generic Laver Diamond
Sean D. Cox
Viale \cite{Viale_GuessingModel} introduced the notion of Generic Laver Diamond at ---which we denote ---asserting the existence of a single function f…