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