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Sean Cox [11]Sean D. Cox [4]
  1.  23
    Characterizing Large Cardinals in Terms of Layered Posets.Sean Cox & Philipp Lücke - 2017 - Annals of Pure and Applied Logic 168 (5):1112-1131.
  2.  13
    Quotients of Strongly Proper Forcings and Guessing Models.Sean Cox & John Krueger - 2016 - Journal of Symbolic Logic 81 (1):264-283.
  3.  5
    Covering Theorems for the Core Model, and an Application to Stationary Set Reflection.Sean Cox - 2010 - Annals of Pure and Applied Logic 161 (1):66-93.
    We prove covering theorems for K, where K is the core model below the sharp for a strong cardinal, and give an application to stationary set reflection.
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  4.  21
    PFA and Ideals on $\omega_{2}$ Whose Associated Forcings Are Proper.Sean Cox - 2012 - Notre Dame Journal of Formal Logic 53 (3):397-412.
    Given an ideal $I$ , let $\mathbb{P}_{I}$ denote the forcing with $I$ -positive sets. We consider models of forcing axioms $MA(\Gamma)$ which also have a normal ideal $I$ with completeness $\omega_{2}$ such that $\mathbb{P}_{I}\in \Gamma$ . Using a bit more than a superhuge cardinal, we produce a model of PFA (proper forcing axiom) which has many ideals on $\omega_{2}$ whose associated forcings are proper; a similar phenomenon is also observed in the standard model of $MA^{+\omega_{1}}(\sigma\mbox{-closed})$ obtained from a supercompact cardinal. (...)
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  5.  6
    Ideal Projections and Forcing Projections.Sean Cox & Martin Zeman - 2014 - Journal of Symbolic Logic 79 (4):1247-1285.
    It is well known that saturation of ideals is closely related to the “antichain-catching” phenomenon from Foreman–Magidor–Shelah [10]. We consider several antichain-catching properties that are weaker than saturation, and prove:If${\cal I}$is a normal ideal on$\omega _2 $which satisfiesstationary antichain catching, then there is an inner model with a Woodin cardinal;For any$n \in \omega $, it is consistent relative to large cardinals that there is a normal ideal${\cal I}$on$\omega _n $which satisfiesprojective antichain catching, yet${\cal I}$is not saturated. This provides a negative (...)
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  6.  5
    Layered Posets and Kunen’s Universal Collapse.Sean Cox - 2019 - Notre Dame Journal of Formal Logic 60 (1):27-60.
    We develop the theory of layered posets and use the notion of layering to prove a new iteration theorem is κ-cc, as long as direct limits are used sufficiently often. This iteration theorem simplifies and generalizes the various chain condition arguments for universal Kunen iterations in the literature on saturated ideals, especially in situations where finite support iterations are not possible. We also provide two applications:1 For any n≥1, a wide variety of <ωn−1-closed, ωn+1-cc posets of size ωn+1 can consistently (...)
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  7.  16
    On the Universality of the Nonstationary Ideal.Sean D. Cox - 2018 - Mathematical Logic Quarterly 64 (1-2):103-117.
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  8.  28
    Consistency Strength of Higher Chang’s Conjecture, Without CH.Sean D. Cox - 2011 - Archive for Mathematical Logic 50 (7-8):759-775.
    We prove that ${(\omega_3, \omega_2) \twoheadrightarrow (\omega_2, \omega_1)}$ implies there is an inner model with a weak repeat measure.
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  9. Compactness Versus Hugeness at Successor Cardinals.Sean Cox & Monroe Eskew - forthcoming - Journal of Mathematical Logic.
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  10. Forcing Axioms, Approachability, and Stationary Set Reflection.Sean D. Cox - 2021 - Journal of Symbolic Logic 86 (2):499-530.
    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 reflection to a version of Strong Chang’s Conjecture cannot be reversed; strengthen and simplify some results of Krueger about forcing axioms and approachability; and prove that some other related results of Krueger are sharp. We also adapt some ideas of Woodin to simplify and unify many arguments in the literature involving preservation of forcing axioms.
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  11.  24
    Knowledge and Information in Global Competition: A New Framework for Classifying and Evaluating Manipulative Communication Techniques.Eldar Sultanow, Sean Cox, Sebastian Homann, Philipp Koch & Olliver Franke - 2016 - International Letters of Social and Humanistic Sciences 72:27-44.
    Source: Author: Eldar Sultanow, Sean Cox, Sebastian Homann, Philipp Koch, Olliver Franke Mass media initiated exhibitions of information and knowledge streams account for a significant factor of opinion-forming in modern digitalized nations and thus influence their country's political development. Within the framework of a globalized environment, this information has the ability to shape worldwide opinion and international policy decisions across geographical boundaries. Similarly, however, information and knowledge that does not flow freely has an impact on the behind the scenes decisions (...)
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  12.  9
    Namba Forcing, Weak Approximation, and Guessing.Sean Cox & John Krueger - 2018 - Journal of Symbolic Logic 83 (4):1539-1565.
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  13.  3
    Nonregular Ultrafilters on Ω2.Sean Cox - 2011 - Journal of Symbolic Logic 76 (3):827-845.
    We obtain lower bounds for the consistency strength of fully nonregular ultrafilters on ω₂.
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  14.  1
    A Variant of Shelah's Characterization of Strong Chang's Conjecture.Sean Cox & Hiroshi Sakai - 2019 - Mathematical Logic Quarterly 65 (2):251-257.
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