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