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polarized partition relation Ostaszewski square Small forcing unbounded function weak diamond Rado's conjecture Partition Relations Slim tree club_AD Analytic sets Ascent Path Reduced Power Coherent tree Strongly compact cardinal Well-behaved magma super-Souslin tree Commutative cancellative semigroups Strong coloring weak square Knaster Almost Souslin Hindman's Theorem OCA Diamond for trees Forcing incompactness strongly bounded groups Selective Ultrafilter Subadditive full tree Parameterized proxy principle Constructible Universe Erdos Cardinal Chromatic number indecomposable filter Rainbow sets Subtle cardinal Uniformly coherent Antichain Ascending path Souslin Tree L-space Foundations Postprocessing function Strongly Luzin set Precaliber coloring number square C-sequence Forcing Axioms xbox Nonspecial tree Local Club Condensation. Successor of Regular Cardinal Sakurai's Bell inequality Reflecting stationary set higher Baire space Almost-disjoint family SNR Singular Density countably metacompact Generalized descriptive set theory stationary reflection Filter reflection Non-saturation Sierpinski's onto mapping principle Distributive tree Minimal Walks transformations free Boolean algebra Fat stationary set Cohen real Cardinal Invariants diamond star Iterated forcing Ineffable cardinal Subtle tree property reflection principles Monotonically far Knaster and friends Square-Brackets Partition Relations Interval topology on trees Axiom R Vanishing levels Amenable C-sequence Singular cofinality Club Guessing HOD Rock n' Roll Entangled linear order Ulam matrix middle diamond free Souslin tree positive partition relation Erdos-Hajnal graphs Hedetniemi's conjecture Singular cardinals combinatorics PFA Luzin set Large Cardinals Uniformization Chang's conjecture AIM forcing Aronszajn tree Lipschitz reduction Ramsey theory over partitions S-Space Jonsson cardinal P-Ideal Dichotomy Sigma-Prikry Open Access weak Kurepa tree PFA(S)[S] Hereditarily Lindelöf space approachability ideal nonmeager set O-space Absoluteness Greatly Mahlo Countryman line perfectly normal Martin's Axiom stationary hitting ZFC construction Forcing with side conditions Dushnik-Miller Universal Sequences very good scale Almost countably chromatic Commutative projection system square principles Closed coloring ccc Fodor-type reflection Partition relations for trees Microscopic Approach 54G20 specializable Souslin tree Uniformly homogeneous Fast club tensor product graph b-scale Kurepa Hypothesis Poset projective Boolean algebra Prevalent singular cardinals Was Ulam right? regressive Souslin tree stick Diamond Successor of Singular Cardinal Shelah's Strong Hypothesis Respecting tree Intersection model Whitehead Problem Weakly compact cardinal Cardinal function Subnormal ideal Mandelbrot set sap GMA Prikry-type forcing Generalized Clubs Diamond-sharp Dowker space
Tag Archives: Souslin Tree
Jensen’s diamond principle and its relatives
This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading
Young Researchers in Set Theory, March 2011
These are the slides of a talk I gave at the Young Researchers in Set Theory 2011 meeting (Königswinter, 21–25 March 2011). Talk Title: Around Jensen’s square principle Abstract: Jensen‘s square principle for a cardinal $\lambda$ asserts the existence of a particular ladder … 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
The Ostaszewski square, and homogeneous Souslin trees
Abstract: Assume GCH and let $\lambda$ denote an uncountable cardinal. We prove that if $\square_\lambda$ holds, then this may be witnessed by a coherent sequence $\left\langle C_\alpha \mid \alpha<\lambda^+\right\rangle$ with the following remarkable guessing property: For every sequence $\langle A_i\mid i<\lambda\rangle$ … Continue reading
Posted in Publications, Souslin Hypothesis, Squares and Diamonds
Tagged 03E05, 03E35, Club Guessing, Fat stationary set, Ostaszewski square, Souslin Tree
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