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