Archives
Keywords
Postprocessing function Hindman's Theorem Almost Souslin stationary reflection Vanishing levels Amenable C-sequence Interval topology on trees Was Ulam right? Fat stationary set Singular cofinality reflection principles Prevalent singular cardinals Ascending path Well-behaved magma Forcing Axioms Non-saturation unbounded function Poset Chang's conjecture Diamond Singular cardinals combinatorics full tree diamond star Shelah's Strong Hypothesis Erdos Cardinal Antichain Ascent Path Strong coloring Subnormal ideal Commutative projection system Hedetniemi's conjecture club_AD Almost countably chromatic Universal Sequences 54G20 square principles Foundations very good scale approachability ideal Dushnik-Miller free Boolean algebra coloring number Successor of Singular Cardinal Jonsson cardinal Intersection model PFA(S)[S] nonmeager set Erdos-Hajnal graphs weak square Selective Ultrafilter stick Uniformly homogeneous xbox Large Cardinals Ineffable cardinal Sierpinski's onto mapping principle Ostaszewski square higher Baire space Minimal Walks Parameterized proxy principle polarized partition relation HOD indecomposable filter Strongly compact cardinal S-Space strongly bounded groups super-Souslin tree Mandelbrot set square Club Guessing Weakly compact cardinal Strongly Luzin set tensor product graph Prikry-type forcing Hereditarily Lindelöf space Fodor-type reflection Luzin set regressive Souslin tree projective Boolean algebra Partition relations for trees stationary hitting Chromatic number Ramsey theory over partitions Whitehead Problem Open Access Analytic sets Uniformization b-scale Countryman line Fast club Constructible Universe Respecting tree Cardinal function C-sequence Diamond for trees specializable Souslin tree Reflecting stationary set Cardinal Invariants Dowker space transformations Rainbow sets ZFC construction L-space weak Kurepa tree Aronszajn tree Martin's Axiom Generalized descriptive set theory perfectly normal countably metacompact O-space Small forcing Successor of Regular Cardinal Iterated forcing Slim tree Knaster and friends Axiom R Entangled linear order SNR Absoluteness Coherent tree Distributive tree Local Club Condensation. Uniformly coherent Partition Relations Singular Density Precaliber Knaster positive partition relation Rado's conjecture Greatly Mahlo weak diamond middle diamond Microscopic Approach Subtle tree property P-Ideal Dichotomy sap Lipschitz reduction free Souslin tree Sigma-Prikry Forcing with side conditions AIM forcing Kurepa Hypothesis Filter reflection Cohen real ccc Subadditive Subtle cardinal Square-Brackets Partition Relations Monotonically far Generalized Clubs Sakurai's Bell inequality Ulam matrix Forcing Nonspecial tree OCA incompactness GMA Reduced Power Diamond-sharp Almost-disjoint family Commutative cancellative semigroups Rock n' Roll PFA Closed coloring Souslin Tree
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
Comments Off on 4th Arctic Set Theory Workshop, January 2019
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
