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