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