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OCA Ulam matrix Universal Sequences Ostaszewski square free Boolean algebra Filter reflection Small forcing very good scale Closed coloring weak diamond Successor of Singular Cardinal tensor product graph Cardinal function Prevalent singular cardinals O-space PFA(S)[S] Selective Ultrafilter Well-behaved magma indecomposable filter projective Boolean algebra HOD Ascending path coloring number AIM forcing Strong coloring Almost-disjoint family b-scale specializable Souslin tree full tree Erdos-Hajnal graphs Large Cardinals Martin's Axiom Sigma-Prikry Reduced Power countably metacompact stick Chang's conjecture Souslin Tree transformations Shelah's Strong Hypothesis Knaster weak square ZFC construction Whitehead Problem Fast club Dowker space diamond star Uniformization Constructible Universe Microscopic Approach Rado's conjecture Subtle cardinal xbox GMA Greatly Mahlo L-space Parameterized proxy principle Subtle tree property Non-saturation Vanishing levels Erdos Cardinal Ascent Path Lipschitz reduction Open Access Fodor-type reflection Sakurai's Bell inequality Postprocessing function Monotonically far Diamond for trees Amenable C-sequence incompactness Diamond free Souslin tree Countryman line Distributive tree Ineffable cardinal Chromatic number polarized partition relation Cardinal Invariants Club Guessing Was Ulam right? stationary reflection strongly bounded groups Ramsey theory over partitions nonmeager set Strongly Luzin set Singular cofinality 54G20 PFA Successor of Regular Cardinal Foundations Slim tree Entangled linear order regressive Souslin tree higher Baire space club_AD Weakly compact cardinal unbounded function Subnormal ideal Uniformly homogeneous Partition Relations Analytic sets S-Space Cohen real Strongly compact cardinal reflection principles Axiom R Absoluteness Hindman's Theorem Rainbow sets Respecting tree Forcing super-Souslin tree approachability ideal Kurepa Hypothesis P-Ideal Dichotomy perfectly normal Prikry-type forcing Jonsson cardinal square principles positive partition relation Aronszajn tree Almost countably chromatic Singular cardinals combinatorics weak Kurepa tree Diamond-sharp Dushnik-Miller Intersection model Mandelbrot set Sierpinski's onto mapping principle Almost Souslin Interval topology on trees C-sequence Luzin set ccc Forcing with side conditions Precaliber Hereditarily Lindelöf space Coherent tree middle diamond Reflecting stationary set Hedetniemi's conjecture Local Club Condensation. Antichain Rock n' Roll Commutative cancellative semigroups stationary hitting SNR Nonspecial tree Knaster and friends Minimal Walks Commutative projection system sap Forcing Axioms Square-Brackets Partition Relations Fat stationary set Uniformly coherent Poset Generalized descriptive set theory Subadditive Generalized Clubs Singular Density Iterated forcing Partition relations for trees square
Tag Archives: Kurepa Hypothesis
Diamond on Kurepa trees
Joint work with Ziemek Kostana and Saharon Shelah. Abstract. We introduce a new weak variation of diamond that is meant to guess only the branches of a Kurepa tree. We demonstrate that this variation is considerably weaker than diamond by … 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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Strong failures of higher analogs of Hindman’s Theorem
Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … Continue reading
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Entangled linear order, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
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Square with built-in diamond-plus
Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in $L$ for every infinite cardinal. As an application, we prove that … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, Respecting tree, square, xbox
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Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading
A Kurepa tree from diamond-plus
Recall that $T$ is said to be a $\kappa$-Kurepa tree if $T$ is a tree of height $\kappa$, whose levels $T_\alpha$ has size $\le|\alpha|$ for co-boundedly many $\alpha<\kappa$, and such that the set of branches of $T$ has size $>\kappa$. … Continue reading
Posted in Blog, Expository
Tagged diamond star, Kurepa Hypothesis
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Kurepa trees and ineffable cardinals
Recall that $T$ is said to be a $\kappa$-Kurepa tree if $T$ is a tree of height $\kappa$, whose levels $T_\alpha$ has size $\le|\alpha|$ for co-boundedly many $\alpha<\kappa$, and such that the set of branches of $T$ has size $>\kappa$. … Continue reading
On guessing generalized clubs at the successors of regulars
Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading
