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Diamond for trees C-sequence O-space club_AD Rado's conjecture coloring number Microscopic Approach Well-behaved magma ZFC construction Subadditive incompactness Shelah's Strong Hypothesis Aronszajn tree unbounded function Uniformly homogeneous PFA weak Kurepa tree Lipschitz reduction Sierpinski's onto mapping principle Singular cofinality polarized partition relation Universal Sequences PFA(S)[S] Almost Souslin HOD countably metacompact SNR Uniformly coherent Prevalent singular cardinals Strongly compact cardinal Knaster Postprocessing function Successor of Singular Cardinal Chang's conjecture L-space reflection principles Axiom R Constructible Universe Strong coloring Fodor-type reflection Small forcing b-scale Fast club AIM forcing Precaliber Foundations GMA Erdos-Hajnal graphs Hedetniemi's conjecture Dushnik-Miller full tree projective Boolean algebra 54G20 Cardinal function sap ccc Erdos Cardinal Chromatic number Subnormal ideal Uniformization Almost countably chromatic Analytic sets Souslin Tree Luzin set stationary reflection very good scale P-Ideal Dichotomy specializable Souslin tree Filter reflection Weakly compact cardinal Parameterized proxy principle stick Nonspecial tree Closed coloring Intersection model Forcing Countryman line Fat stationary set Ineffable cardinal Hereditarily Lindelöf space OCA middle diamond Greatly Mahlo Local Club Condensation. nonmeager set Was Ulam right? Ramsey theory over partitions Subtle tree property Open Access Partition Relations Ulam matrix Amenable C-sequence Antichain Whitehead Problem approachability ideal Slim tree Kurepa Hypothesis Successor of Regular Cardinal tensor product graph regressive Souslin tree Square-Brackets Partition Relations Poset Vanishing levels free Souslin tree Sakurai's Bell inequality Cardinal Invariants Sigma-Prikry Subtle cardinal Prikry-type forcing Jonsson cardinal Generalized Clubs free Boolean algebra weak square Reduced Power Selective Ultrafilter Hindman's Theorem Rainbow sets Absoluteness diamond star Distributive tree weak diamond Strongly Luzin set Generalized descriptive set theory Forcing Axioms Coherent tree Cohen real Club Guessing Large Cardinals Iterated forcing Martin's Axiom Mandelbrot set transformations Singular cardinals combinatorics Knaster and friends stationary hitting Rock n' Roll Dowker space xbox strongly bounded groups square principles Diamond Minimal Walks Respecting tree Almost-disjoint family higher Baire space super-Souslin tree S-Space Commutative projection system Reflecting stationary set Ostaszewski square Diamond-sharp indecomposable ultrafilter square positive partition relation Singular Density Non-saturation Commutative cancellative semigroups Ascent Path
Tag Archives: 03E55
Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Intersection models of generic extensions obtained from a commutative projection systems of notions of forcing has recently regained interest, especially in the study of descriptive set theory. Here, we show that … Continue reading
Posted in Compactness, Preprints
Tagged 03E05, 03E35, 03E55, Ascent Path, C-sequence, Commutative projection system, indecomposable ultrafilter, Intersection model, Strongly compact cardinal
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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
