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