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