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Strong coloring Dushnik-Miller Ramsey theory over partitions stick Dowker space Diamond-sharp Slim tree Greatly Mahlo Singular cofinality Weakly compact cardinal free Souslin tree Mandelbrot set Generalized Clubs Generalized descriptive set theory ZFC construction Uniformly coherent Closed coloring Subtle cardinal projective Boolean algebra Coherent tree Microscopic Approach Rock n' Roll Knaster Knaster and friends Rado's conjecture Club Guessing Martin's Axiom Cardinal Invariants Constructible Universe Ineffable cardinal Parameterized proxy principle Forcing square principles Successor of Regular Cardinal reflection principles Subtle tree property Absoluteness regressive Souslin tree very good scale Sakurai's Bell inequality S-Space Chang's conjecture incompactness Rainbow sets Reduced Power C-sequence xbox sap weak square Fast club stationary hitting Lipschitz reduction positive partition relation weak diamond Ulam matrix GMA Precaliber specializable Souslin tree Foundations AIM forcing Was Ulam right Prevalent singular cardinals Square-Brackets Partition Relations Almost Souslin unbounded function Local Club Condensation. Commutative cancellative semigroups Forcing Axioms PFA(S)[S] approachability ideal Erdos-Hajnal graphs Erdos Cardinal Ostaszewski square Universal Sequences Analytic sets 54G20 middle diamond Cardinal function Almost countably chromatic full tree Filter reflection Fat stationary set Subnormal ideal Jonsson cardinal club_AD Reflecting stationary set Nonspecial tree Sierpinski's onto mapping principle Luzin set Fodor-type reflection O-space Postprocessing function Hedetniemi's conjecture Chromatic number strongly bounded groups Almost-disjoint family Kurepa Hypothesis Souslin Tree P-Ideal Dichotomy Hereditarily Lindelöf space ccc diamond star SNR Singular Density Sigma-Prikry transformations Cohen real Singular cardinals combinatorics Minimal Walks nonmeager set Poset Open Access tensor product graph higher Baire space Iterated forcing Hindman's Theorem Diamond Amenable C-sequence HOD stationary reflection Shelah's Strong Hypothesis polarized partition relation Subadditive Antichain Partition Relations Small forcing PFA Uniformly homogeneous Distributive tree weak Kurepa tree b-scale free Boolean algebra Vanishing levels Aronszajn tree Whitehead Problem Selective Ultrafilter Axiom R indecomposable ultrafilter Prikry-type forcing Large Cardinals Diamond for trees OCA square Strongly Luzin set Successor of Singular Cardinal super-Souslin tree countably metacompact Well-behaved magma Non-saturation L-space Uniformization coloring number Ascent Path
Tag Archives: 03E35
The failure of diamond on a reflecting stationary set
Joint work with Moti Gitik. Abstract: It is shown that the failure of $\diamondsuit_S$, for a subset $S\subseteq\aleph_{\omega+1}$ that reflects stationarily often, is consistent with GCH and $\text{AP}_{\aleph_\omega}$, relatively to the existence of a supercompact cardinal. This should be comapred with … 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
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
Antichains in partially ordered sets of singular cofinality
Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The main result of of this … Continue reading
Posted in Publications, Singular Cardinals Combinatorics
Tagged 03E04, 03E35, 06A07, Antichain, Poset, Singular cofinality
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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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