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Cardinal function indecomposable filter full tree higher Baire space Iterated forcing Commutative projection system Constructible Universe tensor product graph Generalized descriptive set theory specializable Souslin tree Mandelbrot set Almost countably chromatic Luzin set OCA diamond star Singular cardinals combinatorics Coherent tree weak diamond Square-Brackets Partition Relations nonmeager set transformations strongly bounded groups S-Space Fat stationary set Forcing P-Ideal Dichotomy Reflecting stationary set ccc Erdos Cardinal Countryman line Ramsey theory over partitions Axiom R Respecting tree b-scale Dushnik-Miller very good scale Hereditarily Lindelöf space xbox HOD Generalized Clubs Sakurai's Bell inequality approachability ideal Knaster Parameterized proxy principle Fast club Subtle cardinal Uniformly coherent Closed coloring Universal Sequences Martin's Axiom Jonsson cardinal Shelah's Strong Hypothesis Lipschitz reduction Absoluteness Souslin Tree sap coloring number Monotonically far Minimal Walks Uniformly homogeneous Precaliber weak square GMA Partition Relations Dowker space Nonspecial tree Local Club Condensation. club_AD Non-saturation stationary reflection Kurepa Hypothesis Successor of Singular Cardinal Small forcing Forcing with side conditions PFA(S)[S] Almost Souslin Sierpinski's onto mapping principle Ulam matrix Ostaszewski square Uniformization Intersection model Commutative cancellative semigroups Diamond for trees Greatly Mahlo Fodor-type reflection PFA ZFC construction Entangled linear order C-sequence Analytic sets free Boolean algebra Large Cardinals Prevalent singular cardinals polarized partition relation Diamond-sharp Slim tree Strongly compact cardinal Hedetniemi's conjecture Singular cofinality AIM forcing Distributive tree Prikry-type forcing reflection principles Open Access projective Boolean algebra Forcing Axioms Was Ulam right? Erdos-Hajnal graphs stick Cohen real Vanishing levels Subnormal ideal Club Guessing Antichain Diamond Reduced Power SNR Selective Ultrafilter Rado's conjecture Successor of Regular Cardinal square principles O-space Weakly compact cardinal square Rock n' Roll Ascent Path incompactness Subtle tree property unbounded function Strong coloring 54G20 Interval topology on trees Partition relations for trees Amenable C-sequence stationary hitting Hindman's Theorem Aronszajn tree middle diamond super-Souslin tree Sigma-Prikry Rainbow sets regressive Souslin tree Poset Chang's conjecture Foundations Knaster and friends Ascending path Postprocessing function Chromatic number Filter reflection Subadditive Microscopic Approach Cardinal Invariants Well-behaved magma perfectly normal countably metacompact Singular Density weak Kurepa tree L-space Whitehead Problem Ineffable cardinal positive partition relation free Souslin tree Almost-disjoint family Strongly Luzin set
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
