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Knaster and friends free Souslin tree Generalized Clubs Antichain reflection principles specializable Souslin tree square principles tensor product graph Foundations Greatly Mahlo Poset Distributive tree O-space middle diamond S-Space Strongly Luzin set Hedetniemi's conjecture weak diamond Cohen real Rainbow sets Absoluteness weak Kurepa tree Amenable C-sequence Jonsson cardinal Almost-disjoint family Commutative cancellative semigroups Reflecting stationary set stick Successor of Singular Cardinal strongly bounded groups Luzin set Cardinal Invariants nonmeager set Small forcing regressive Souslin tree ccc coloring number L-space Subadditive polarized partition relation Microscopic Approach Rock n' Roll Axiom R Weakly compact cardinal Ineffable cardinal Chromatic number Subtle tree property xbox Chang's conjecture Large Cardinals Fodor-type reflection Forcing Axioms PFA Erdos Cardinal weak square unbounded function projective Boolean algebra Hereditarily Lindelöf space Countryman line b-scale stationary hitting Local Club Condensation. Precaliber Non-saturation incompactness Almost countably chromatic Forcing Cardinal function Whitehead Problem Ulam matrix Commutative projection system Partition Relations stationary reflection AIM forcing Souslin Tree Mandelbrot set Ascent Path Shelah's Strong Hypothesis Singular cardinals combinatorics Rado's conjecture super-Souslin tree SNR sap Respecting tree Diamond-sharp HOD Club Guessing indecomposable filter Dowker space Square-Brackets Partition Relations diamond star Aronszajn tree Generalized descriptive set theory 54G20 Kurepa Hypothesis Intersection model OCA club_AD Closed coloring Martin's Axiom Strongly compact cardinal Erdos-Hajnal graphs Dushnik-Miller square Diamond for trees very good scale Singular cofinality Nonspecial tree Postprocessing function Coherent tree Well-behaved magma GMA full tree Parameterized proxy principle Vanishing levels countably metacompact P-Ideal Dichotomy Open Access Fat stationary set Uniformly coherent Ostaszewski square positive partition relation Uniformly homogeneous transformations Minimal Walks Sakurai's Bell inequality Diamond Fast club higher Baire space Subtle cardinal ZFC construction Slim tree Was Ulam right? Lipschitz reduction Universal Sequences Selective Ultrafilter Analytic sets free Boolean algebra C-sequence approachability ideal Subnormal ideal Prevalent singular cardinals Hindman's Theorem Iterated forcing Singular Density Knaster Sigma-Prikry Reduced Power Ramsey theory over partitions Filter reflection Successor of Regular Cardinal Uniformization Sierpinski's onto mapping principle Strong coloring Prikry-type forcing Almost Souslin PFA(S)[S] Constructible Universe
Author Archives: Assaf Rinot
May the successor of a singular cardinal be Jonsson?
Abstract: We collect necessary conditions for the successor of a singular cardinal to be Jónsson.
Posted in Open Problems, Singular Cardinals Combinatorics
Tagged Jonsson cardinal
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Perspectives on Set Theory, November 2023
I gave an invited talk at the Perspectives on Set Theory conference, November 2023. Talk Title: May the successor of a singular cardinal be Jónsson? Abstract: We’ll survey what’s known about the question in the title and collect ten open … Continue reading
Posted in Invited Talks, Open Problems
Tagged Jonsson cardinal, Successor of Singular Cardinal
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The vanishing levels of a tree
Joint work with Shira Yadai and Zhixing You. Abstract. We initiate the study of the spectrum of sets that can be realized as the vanishing levels
Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A
A counterexample related to a theorem of Komjáth and Weiss
Joint work with Rodrigo Rey Carvalho. Abstract. In a paper from 1987, Komjath and Weiss proved that for every regular topological space
Posted in Partition Relations, Preprints, Topology
Tagged 03E02, 54G20, Prikry-type forcing, ZFC construction
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A Shelah group in ZFC
Joint work with Márk Poór. Abstract. In a paper from 1980, Shelah constructed an uncountable group all of whose proper subgroups are countable. Assuming the continuum hypothesis, he constructed an uncountable group
Posted in Groups, Publications
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
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Gdańsk Logic Conference, May 2023
I gave an invited talk at the first Gdańsk Logic Conference, May 2023. Talk Title: Was Ulam right? Abstract: An Ulam matrix is one of the earliest gems of infinite combinatorics. Around the same time of its discovery, another Polish … Continue reading
A series of lectures on Club_AD, February–March 2023
As part of the Thematic Program on Set Theoretic Methods in Algebra, Dynamics and Geometry (Fields Institute, January–June, 2023), Spencer Unger and I delivered a Graduate Course on Set Theory, Algebra and Analysis. My part of the course was a … Continue reading
Winter School in Abstract Analysis, January 2023
I gave a 3-lecture tutorial at the Winter School in Abstract Analysis in Steken, January 2023. Title: Club guessing Abstract. Club guessing principles were introduced by Shelah as a weakening of Jensen’s diamond. Most spectacularly, they were used to prove … Continue reading
