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