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