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Was Ulam right? Local Club Condensation. super-Souslin tree Foundations Universal Sequences PFA(S)[S] b-scale Absoluteness Intersection model reflection principles Axiom R Hindman's Theorem Successor of Singular Cardinal Erdos-Hajnal graphs Knaster and friends Chang's conjecture Square-Brackets Partition Relations full tree Parameterized proxy principle Chromatic number Almost Souslin stationary reflection Weakly compact cardinal positive partition relation Entangled linear order Non-saturation Strongly Luzin set Sigma-Prikry Hereditarily Lindelöf space regressive Souslin tree Partition relations for trees Reflecting stationary set Reduced Power Martin's Axiom Small forcing Strongly compact cardinal Prevalent singular cardinals Luzin set Forcing with side conditions ccc Generalized descriptive set theory sap Coherent tree projective Boolean algebra Singular cardinals combinatorics Whitehead Problem Vanishing levels Cardinal Invariants Kurepa Hypothesis Almost-disjoint family Subtle tree property Rock n' Roll Open Access Iterated forcing weak Kurepa tree Diamond AIM forcing Commutative cancellative semigroups Fodor-type reflection club_AD Filter reflection Successor of Regular Cardinal Erdos Cardinal Distributive tree Interval topology on trees coloring number square stick indecomposable filter strongly bounded groups SNR Almost countably chromatic Sierpinski's onto mapping principle Monotonically far Hedetniemi's conjecture countably metacompact Singular cofinality Uniformization Minimal Walks Countryman line Cohen real Amenable C-sequence 54G20 Club Guessing Nonspecial tree Greatly Mahlo GMA perfectly normal xbox Dushnik-Miller Subnormal ideal Dowker space Ineffable cardinal Ascent Path weak diamond Singular Density free Souslin tree Large Cardinals polarized partition relation Partition Relations square principles Subadditive Jonsson cardinal weak square specializable Souslin tree transformations incompactness Precaliber Mandelbrot set Postprocessing function nonmeager set Commutative projection system Slim tree tensor product graph L-space Fat stationary set Aronszajn tree free Boolean algebra Diamond-sharp Analytic sets Shelah's Strong Hypothesis OCA Microscopic Approach Selective Ultrafilter diamond star Forcing PFA Antichain higher Baire space Well-behaved magma stationary hitting unbounded function Uniformly homogeneous Lipschitz reduction Constructible Universe HOD Souslin Tree very good scale Forcing Axioms Ascending path Sakurai's Bell inequality Fast club Rainbow sets O-space Closed coloring P-Ideal Dichotomy Uniformly coherent Poset ZFC construction Knaster Subtle cardinal C-sequence Diamond for trees approachability ideal Rado's conjecture Ulam matrix Respecting tree Prikry-type forcing Ostaszewski square Ramsey theory over partitions middle diamond Generalized Clubs Cardinal function S-Space Strong coloring
Tag Archives: Club Guessing
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
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
Transforming rectangles into squares, with applications to strong colorings
Abstract: It is proved that every singular cardinal $\lambda$ admits a function $\textbf{rts}:[\lambda^+]^2\rightarrow[\lambda^+]^2$ that transforms rectangles into squares. That is, whenever $A,B$ are cofinal subsets of $\lambda^+$, we have $\textbf{rts}[A\circledast B]\supseteq C\circledast C$, for some cofinal subset $C\subseteq\lambda^+$. As a … 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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