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Sigma-Prikry Poset AIM forcing Rainbow sets weak square ccc Postprocessing function Prevalent singular cardinals square super-Souslin tree SNR Subtle cardinal positive partition relation Cardinal function Jonsson cardinal very good scale weak Kurepa tree Hereditarily Lindelöf space Foundations Ulam matrix Distributive tree PFA Countryman line Ramsey theory over partitions Hindman's Theorem unbounded function Axiom R Almost countably chromatic Lipschitz reduction Large Cardinals Iterated forcing Uniformly coherent Fat stationary set Subadditive middle diamond Constructible Universe approachability ideal P-Ideal Dichotomy xbox projective Boolean algebra Almost-disjoint family L-space Hedetniemi's conjecture O-space Rock n' Roll Intersection model Strongly Luzin set HOD Successor of Regular Cardinal Microscopic Approach full tree Commutative cancellative semigroups Forcing Mandelbrot set coloring number Forcing Axioms Knaster Well-behaved magma Square-Brackets Partition Relations Diamond for trees nonmeager set Analytic sets Chromatic number square principles Dowker space Singular Density GMA reflection principles Weakly compact cardinal C-sequence Knaster and friends Was Ulam right? Almost Souslin Generalized descriptive set theory diamond star Slim tree Commutative projection system Shelah's Strong Hypothesis Sakurai's Bell inequality Greatly Mahlo indecomposable filter Prikry-type forcing Souslin Tree Coherent tree stick Subnormal ideal Luzin set free Souslin tree Antichain countably metacompact Successor of Singular Cardinal Parameterized proxy principle Vanishing levels Small forcing Partition Relations OCA Nonspecial tree Cardinal Invariants stationary reflection club_AD Whitehead Problem specializable Souslin tree Diamond Uniformly homogeneous Fast club Absoluteness Sierpinski's onto mapping principle Reflecting stationary set strongly bounded groups Strong coloring sap Singular cofinality Ascent Path Fodor-type reflection incompactness Rado's conjecture b-scale higher Baire space Amenable C-sequence Generalized Clubs 54G20 Ineffable cardinal Respecting tree stationary hitting Aronszajn tree tensor product graph Open Access Reduced Power polarized partition relation transformations Local Club Condensation. Subtle tree property Closed coloring Cohen real ZFC construction PFA(S)[S] Selective Ultrafilter Chang's conjecture Uniformization Strongly compact cardinal free Boolean algebra Filter reflection S-Space Ostaszewski square Kurepa Hypothesis Non-saturation Singular cardinals combinatorics Diamond-sharp Universal Sequences Erdos Cardinal Club Guessing Dushnik-Miller weak diamond Precaliber regressive Souslin tree Erdos-Hajnal graphs Minimal Walks Martin's Axiom
Author Archives: Assaf Rinot
Knaster and friends II: The C-sequence number
Joint work with Chris Lambie-Hanson. Abstract. Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable … Continue reading
The 15th International Workshop on Set Theory in Luminy, September 2019
I gave an invited talk at the 15th International Workshop on Set Theory in Luminy in Marseille, September 2019. Talk Title: Chain conditions, unbounded colorings and the C-sequence spectrum. Abstract: The productivity of the
Posted in Invited Talks
Tagged Closed coloring, Knaster, Precaliber, stationary reflection, unbounded function
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Sigma-Prikry forcing I: The Axioms
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. We introduce a class of notions of forcing which we call
Inclusion modulo nonstationary
Joint work with Gabriel Fernandes and Miguel Moreno. Abstract. A classical theorem of Hechler asserts that the structure
50 Years of Set Theory in Toronto, May 2019
I gave an invited talk at the 50 Years of Set Theory in Toronto meeting, Fields Institute for Research in Mathematical Sciences, May 2019. Talk Title: Analytic quasi-orders and two forms of diamond Abstract: We study Borel reduction of equivalence relations … Continue reading
Posted in Invited Talks
Tagged Analytic sets, Diamond-sharp, Generalized descriptive set theory
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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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Souslin trees at successors of regular cardinals
Abstract. We present a weak sufficient condition for the existence of Souslin trees at successor of regular cardinals. The result is optimal and simultaneously improves an old theorem of Gregory and a more recent theorem of the author. Downloads: Citation … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged Parameterized proxy principle, Souslin Tree
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11th Young Set Theory Workshop, June 2018
I gave a 4-lecture tutorial at the 11th Young Set Theory Workshop, Lausanne, June 2018. Title: In praise of C-sequences. Abstract. Ulam and Solovay showed that any stationary set may be split into two. Is it also the case that … Continue reading
Posted in Invited Talks
Tagged Aronszajn tree, C-sequence, incompactness, Knaster, Minimal Walks, Postprocessing function, square
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Knaster and friends I: Closed colorings and precalibers
Joint work with Chris Lambie-Hanson. Abstract. The productivity of the
