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indecomposable ultrafilter Singular cofinality weak diamond Slim tree HOD Postprocessing function free Souslin tree Constructible Universe Hereditarily Lindelöf space Jonsson cardinal Partition Relations Strongly Luzin set OCA b-scale S-Space Almost countably chromatic Foundations Cardinal Invariants Prevalent singular cardinals Ramsey theory over partitions square approachability ideal Minimal Walks Was Ulam right O-space Forcing Fodor-type reflection stick incompactness Ostaszewski square ZFC construction Lipschitz reduction Rado's conjecture Club Guessing Dowker space Rock n' Roll Ascent Path Vanishing levels very good scale countably metacompact SNR Closed coloring Kurepa Hypothesis Amenable C-sequence Chang's conjecture diamond star Reflecting stationary set Small forcing Axiom R Subtle cardinal Non-saturation reflection principles Successor of Regular Cardinal tensor product graph Martin's Axiom Erdos Cardinal Uniformly homogeneous Commutative cancellative semigroups square principles Square-Brackets Partition Relations PFA Well-behaved magma Filter reflection sap Sierpinski's onto mapping principle Absoluteness Iterated forcing Aronszajn tree Large Cardinals Coherent tree Diamond PFA(S)[S] Uniformization Selective Ultrafilter Local Club Condensation. coloring number Hindman's Theorem Subtle tree property Strong coloring Precaliber transformations Ineffable cardinal super-Souslin tree Subadditive Microscopic Approach Successor of Singular Cardinal full tree AIM forcing Diamond for trees stationary hitting specializable Souslin tree Singular Density weak square higher Baire space Universal Sequences Dushnik-Miller Fat stationary set Singular cardinals combinatorics C-sequence Distributive tree strongly bounded groups nonmeager set middle diamond Fast club weak Kurepa tree GMA Ulam matrix Analytic sets projective Boolean algebra Mandelbrot set Whitehead Problem Chromatic number P-Ideal Dichotomy Almost Souslin positive partition relation Almost-disjoint family Weakly compact cardinal Reduced Power Knaster Luzin set Shelah's Strong Hypothesis Open Access Forcing Axioms xbox Generalized descriptive set theory Poset Knaster and friends stationary reflection Rainbow sets Cardinal function Erdos-Hajnal graphs ccc Sigma-Prikry Uniformly coherent Diamond-sharp Generalized Clubs Sakurai's Bell inequality Parameterized proxy principle unbounded function Antichain Nonspecial tree regressive Souslin tree 54G20 L-space Hedetniemi's conjecture polarized partition relation free Boolean algebra Greatly Mahlo club_AD Souslin Tree Subnormal ideal Prikry-type forcing Cohen real
Tag Archives: 03E55
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, 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
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