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Uniformly coherent Luzin set Ascent Path Was Ulam right Subtle cardinal free Boolean algebra Amenable C-sequence club_AD Closed coloring stick Forcing Chromatic number nonmeager set Forcing Axioms free Souslin tree Slim tree SNR Successor of Regular Cardinal Open Access Reflecting stationary set Ulam matrix S-Space Intersection model b-scale Rock n' Roll countably metacompact Almost Souslin Selective Ultrafilter Parameterized proxy principle Erdos Cardinal Uniformly homogeneous Club Guessing weak square Generalized descriptive set theory xbox Nonspecial tree Uniformization Sigma-Prikry Fodor-type reflection Square-Brackets Partition Relations projective Boolean algebra Subtle tree property Martin's Axiom Singular cofinality regressive Souslin tree Dowker space Distributive tree higher Baire space sap specializable Souslin tree polarized partition relation ccc Sakurai's Bell inequality full tree Analytic sets Strongly compact cardinal Hereditarily Lindelöf space Microscopic Approach HOD Filter reflection reflection principles Aronszajn tree Diamond Axiom R Subadditive strongly bounded groups Almost-disjoint family Countryman line Poset tensor product graph approachability ideal super-Souslin tree Singular Density Rado's conjecture Partition Relations AIM forcing Respecting tree Minimal Walks L-space Greatly Mahlo Cardinal Invariants Generalized Clubs Hindman's Theorem Erdos-Hajnal graphs Shelah's Strong Hypothesis Singular cardinals combinatorics Strong coloring Cohen real Sierpinski's onto mapping principle Ramsey theory over partitions Almost countably chromatic Vanishing levels Subnormal ideal Strongly Luzin set Iterated forcing Well-behaved magma Chang's conjecture Absoluteness GMA Fast club stationary hitting stationary reflection PFA(S)[S] Prevalent singular cardinals middle diamond Hedetniemi's conjecture incompactness Cardinal function transformations weak diamond Large Cardinals Rainbow sets very good scale Commutative cancellative semigroups indecomposable ultrafilter ZFC construction Ostaszewski square P-Ideal Dichotomy unbounded function Whitehead Problem Knaster and friends Foundations diamond star Prikry-type forcing square Successor of Singular Cardinal square principles Ineffable cardinal O-space 54G20 C-sequence Small forcing positive partition relation Universal Sequences Jonsson cardinal Mandelbrot set Precaliber Souslin Tree Dushnik-Miller Commutative projection system Lipschitz reduction Knaster Kurepa Hypothesis Reduced Power Constructible Universe Postprocessing function PFA Fat stationary set Non-saturation Coherent tree coloring number Weakly compact cardinal Local Club Condensation. Diamond for trees OCA Antichain weak Kurepa tree Diamond-sharp
Tag Archives: diamond star
Square with built-in diamond-plus
Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in $L$ for every infinite cardinal. As an application, we prove that … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, Respecting tree, square, xbox
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A Kurepa tree from diamond-plus
Recall that $T$ is said to be a $\kappa$-Kurepa tree if $T$ is a tree of height $\kappa$, whose levels $T_\alpha$ has size $\le|\alpha|$ for co-boundedly many $\alpha<\kappa$, and such that the set of branches of $T$ has size $>\kappa$. … Continue reading
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
A relative of the approachability ideal, diamond and non-saturation
Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading
