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