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