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Dowker space transformations weak diamond Prikry-type forcing Absoluteness stationary reflection OCA Whitehead Problem Subtle cardinal Reflecting stationary set Iterated forcing Chromatic number projective Boolean algebra Selective Ultrafilter Rock n' Roll Aronszajn tree higher Baire space Mandelbrot set Kurepa Hypothesis Local Club Condensation. Uniformly homogeneous Interval topology on trees Ramsey theory over partitions AIM forcing Ascent Path weak Kurepa tree Monotonically far Club Guessing super-Souslin tree Reduced Power Shelah's Strong Hypothesis Diamond-sharp weak square square Generalized descriptive set theory Partition relations for trees middle diamond Ineffable cardinal Closed coloring specializable Souslin tree Ascending path Generalized Clubs Knaster and friends Diamond Slim tree Intersection model Fat stationary set Rainbow sets ccc sap O-space Commutative cancellative semigroups Baumgartner's square Lipschitz reduction Coherent tree Distributive tree Ostaszewski square Antichain Cardinal Invariants Nonspecial tree Uniformization free Souslin tree Respecting tree stationary hitting free Boolean algebra Sakurai's Bell inequality tensor product graph xbox Subadditive Poset L-space Partition Relations Was Ulam right? Greatly Mahlo Commutative projection system club_AD 54G20 Almost countably chromatic HOD Almost-disjoint family b-scale Microscopic Approach Dushnik-Miller Forcing Axioms Precaliber Small forcing Axiom R strongly bounded groups P-Ideal Dichotomy Uniformly coherent Amenable C-sequence GMA Postprocessing function Chang's conjecture Non-saturation coloring number Martin's Axiom Fodor-type reflection Prevalent singular cardinals approachability ideal Vanishing levels reflection principles Minimal Walks unbounded function Souslin Tree SNR Well-behaved magma Cohen real regressive Souslin tree perfectly normal Countryman line Analytic sets Diamond for trees Erdos-Hajnal graphs PFA(S)[S] Hereditarily Lindelöf space incompactness Singular cofinality Fast club Sigma-Prikry Filter reflection C-sequence Foundations Ulam matrix Knaster full tree indecomposable filter Almost Souslin S-Space Universal Sequences Square-Brackets Partition Relations Successor of Singular Cardinal Luzin set Hedetniemi's conjecture PFA Constructible Universe Strongly Luzin set Forcing Weakly compact cardinal Hindman's Theorem Parameterized proxy principle Singular cardinals combinatorics Strongly compact cardinal Erdos Cardinal nonmeager set countably metacompact Subtle tree property Sierpinski's onto mapping principle Open Access Forcing with side conditions Rado's conjecture Large Cardinals diamond star Subnormal ideal Jonsson cardinal Entangled linear order square principles Strong coloring very good scale polarized partition relation Cardinal function stick ZFC construction Singular Density positive partition relation Successor of Regular Cardinal
Tag Archives: 03E55
Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Answering a question of Ketonen from the late 1970’s, it is proved that a weakly compact cardinal carrying an indecomposable ultrafilter need not be measurable. The result is obtained by analyzing … Continue reading
Was Ulam right? II: Small width and general ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Sierpinski-type colourings. In contrast to the prequel paper, we focus here on colourings for ideals stratified by their completeness degree. In particular, improving upon Ulam’s theorem and its extension … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E35, 03E55, C-sequence, Kurepa Hypothesis, Open Access, Subnormal ideal, Ulam matrix, Was Ulam right?
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Was Ulam right? I: Basic theory and subnormal ideals
Joint work with Tanmay Inamdar. Abstract. We introduce various coloring principles which generalize the so-called onto mapping principle of Sierpinski to larger cardinals and general ideals. We prove that these principles capture the notion of an Ulam matrix and allow … Continue reading
Knaster and friends II: The C-sequence number
Joint work with Chris Lambie-Hanson. Abstract. Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable … Continue reading
Openly generated Boolean algebras and the Fodor-type reflection principle
Joint work with Sakaé Fuchino. Abstract: We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is $\aleph _2$-projective. Previously it was known that this … Continue reading
Posted in Compactness, Publications
Tagged 03E35, 03E55, 03E65, 03E75, 03G05, 06E05, Axiom R, Fodor-type reflection, free Boolean algebra, projective Boolean algebra, Shelah's Strong Hypothesis, stationary reflection
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On the consistency strength of the Milner-Sauer conjecture
Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading
