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O-space positive partition relation L-space Absoluteness Local Club Condensation. Selective Ultrafilter Erdos-Hajnal graphs indecomposable ultrafilter Jonsson cardinal Erdos Cardinal S-Space countably metacompact Well-behaved magma Cardinal function Generalized Clubs Knaster Uniformly homogeneous Forcing Chromatic number HOD Generalized descriptive set theory Subnormal ideal Singular Density Rado's conjecture Souslin Tree Microscopic Approach Antichain Ramsey theory over partitions Coherent tree free Boolean algebra Whitehead Problem Iterated forcing Prevalent singular cardinals nonmeager set Mandelbrot set Hedetniemi's conjecture Dushnik-Miller Ascent Path Cohen real PFA higher Baire space Non-saturation Sakurai's Bell inequality Diamond-sharp Fat stationary set weak diamond Cardinal Invariants tensor product graph Luzin set Singular cofinality Knaster and friends Ulam matrix free Souslin tree Parameterized proxy principle Lipschitz reduction specializable Souslin tree Ineffable cardinal Kurepa Hypothesis Successor of Regular Cardinal Minimal Walks Was Ulam right Sigma-Prikry Nonspecial tree coloring number very good scale ZFC construction Strong coloring Almost Souslin Rainbow sets Dowker space Prikry-type forcing Filter reflection Small forcing Subadditive Amenable C-sequence Fast club Square-Brackets Partition Relations Uniformly coherent middle diamond Subtle tree property Almost countably chromatic Universal Sequences Vanishing levels Shelah's Strong Hypothesis Weakly compact cardinal C-sequence diamond star Club Guessing Precaliber Greatly Mahlo Postprocessing function Hereditarily Lindelöf space Constructible Universe Uniformization Martin's Axiom Diamond for trees Ostaszewski square projective Boolean algebra full tree transformations xbox Aronszajn tree approachability ideal Almost-disjoint family Rock n' Roll Axiom R 54G20 weak Kurepa tree strongly bounded groups Commutative cancellative semigroups Slim tree square principles incompactness Analytic sets Partition Relations Diamond ccc Foundations Sierpinski's onto mapping principle polarized partition relation P-Ideal Dichotomy GMA OCA Large Cardinals Reduced Power Successor of Singular Cardinal Distributive tree sap square Hindman's Theorem stationary hitting stationary reflection Open Access club_AD Closed coloring Poset SNR reflection principles Chang's conjecture b-scale super-Souslin tree Strongly Luzin set regressive Souslin tree PFA(S)[S] Reflecting stationary set unbounded function AIM forcing stick weak square Fodor-type reflection Singular cardinals combinatorics Forcing Axioms Subtle cardinal
Tag Archives: very good scale
Partitioning a reflecting stationary set
Joint work with Maxwell Levine. Abstract. We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinals combinatorics, we infer … Continue reading
4th Arctic Set Theory Workshop, January 2019
I gave an invited talk at the Arctic Set Theory Workshop 4 in Kilpisjärvi, January 2019. Talk Title: Splitting a stationary set: Is there another way? Abstract: Motivated by a problem in pcf theory, we seek for a new way … Continue reading
Posted in Invited Talks
Tagged Club Guessing, Reflecting stationary set, Ulam matrix, very good scale
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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