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Successor of Regular Cardinal Parameterized proxy principle Erdos Cardinal Club Guessing Chang's conjecture Dowker space Successor of Singular Cardinal Nonspecial tree Microscopic Approach strongly bounded groups Jonsson cardinal Non-saturation P-Ideal Dichotomy unbounded function tensor product graph Almost Souslin Prikry-type forcing Chromatic number square principles club_AD free Souslin tree SNR approachability ideal weak Kurepa tree Reflecting stationary set incompactness Open Access Strong coloring Almost-disjoint family Whitehead Problem Cohen real Knaster Analytic sets reflection principles PFA stationary reflection Fat stationary set Minimal Walks Prevalent singular cardinals Sakurai's Bell inequality Was Ulam right? Square-Brackets Partition Relations Rado's conjecture free Boolean algebra Martin's Axiom Foundations OCA Subadditive b-scale Weakly compact cardinal diamond star Precaliber AIM forcing sap Subnormal ideal Vanishing levels Almost countably chromatic indecomposable ultrafilter Hereditarily Lindelöf space stick Rock n' Roll Small forcing Selective Ultrafilter O-space GMA nonmeager set full tree Ostaszewski square coloring number Cardinal function Respecting tree Coherent tree projective Boolean algebra HOD Fodor-type reflection Lipschitz reduction Antichain Forcing Aronszajn tree Slim tree S-Space Ascent Path Ulam matrix transformations Subtle tree property Sigma-Prikry Commutative cancellative semigroups Absoluteness Erdos-Hajnal graphs Postprocessing function Diamond-sharp specializable Souslin tree Universal Sequences L-space Iterated forcing Commutative projection system Ramsey theory over partitions weak square Shelah's Strong Hypothesis Closed coloring Strongly Luzin set C-sequence Luzin set very good scale Dushnik-Miller Rainbow sets Poset Uniformly homogeneous Uniformization Generalized Clubs Filter reflection Hindman's Theorem Hedetniemi's conjecture Constructible Universe Diamond for trees ZFC construction 54G20 Singular cardinals combinatorics Countryman line higher Baire space Subtle cardinal Large Cardinals Ineffable cardinal countably metacompact square Generalized descriptive set theory Reduced Power Well-behaved magma Diamond Kurepa Hypothesis regressive Souslin tree Singular Density Intersection model Sierpinski's onto mapping principle super-Souslin tree Forcing Axioms Singular cofinality xbox Cardinal Invariants ccc Strongly compact cardinal Mandelbrot set Souslin Tree Uniformly coherent Amenable C-sequence positive partition relation middle diamond Distributive tree Fast club weak diamond polarized partition relation PFA(S)[S] Axiom R Knaster and friends Local Club Condensation. stationary hitting Greatly Mahlo Partition Relations
Tag Archives: P-Ideal Dichotomy
Knaster and friends III: Subadditive colorings
Joint work with Chris Lambie-Hanson. Abstract. We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals
The S-space problem, and the cardinal invariant
Recall that an
Posted in Blog, Expository, Open Problems
Tagged Hereditarily Lindelöf space, P-Ideal Dichotomy, PFA(S)[S], S-Space
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The P-Ideal Dichotomy and the Souslin Hypothesis
John Krueger is visiting Toronto these days, and in a conversation today, we asked ourselves how do one prove the Abraham-Todorcevic theorem that PID implies SH. Namely, that the next statement implies that there are no Souslin trees: Definition. The … Continue reading
Dushnik-Miller for regular cardinals (part 3)
Here is what we already know about the Dushnik-Miller theorem in the case of
