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