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