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