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Axiom R Subnormal ideal Successor of Singular Cardinal Souslin Tree Ascent Path Rainbow sets Partition relations for trees Vanishing levels square Rado's conjecture Singular Density Reflecting stationary set Almost-disjoint family Amenable C-sequence S-Space Forcing Axioms weak diamond Successor of Regular Cardinal PFA(S)[S] Almost countably chromatic Fodor-type reflection Filter reflection Mandelbrot set Antichain Cohen real Diamond-sharp Universal Sequences Chang's conjecture sap Reduced Power strongly bounded groups Entangled linear order Generalized Clubs Ulam matrix Uniformly homogeneous Forcing with side conditions xbox specializable Souslin tree Ascending path Jonsson cardinal GMA Diamond Large Cardinals C-sequence Local Club Condensation. Lipschitz reduction Diamond for trees Subadditive Selective Ultrafilter reflection principles Absoluteness higher Baire space Analytic sets Prevalent singular cardinals unbounded function Was Ulam right? indecomposable filter Open Access Uniformization Singular cofinality perfectly normal countably metacompact square principles Strongly Luzin set Almost Souslin Kurepa Hypothesis Distributive tree SNR ccc regressive Souslin tree Commutative cancellative semigroups Precaliber Constructible Universe stationary hitting Small forcing Well-behaved magma P-Ideal Dichotomy diamond star Foundations OCA Martin's Axiom Shelah's Strong Hypothesis Subtle tree property Postprocessing function Cardinal Invariants Hedetniemi's conjecture Poset middle diamond Strong coloring 54G20 full tree Parameterized proxy principle Aronszajn tree Countryman line positive partition relation projective Boolean algebra Iterated forcing Slim tree incompactness tensor product graph Subtle cardinal HOD Luzin set Strongly compact cardinal Interval topology on trees super-Souslin tree PFA Forcing Sakurai's Bell inequality Intersection model Prikry-type forcing Square-Brackets Partition Relations transformations Microscopic Approach L-space approachability ideal Club Guessing Ineffable cardinal Respecting tree Hindman's Theorem Rock n' Roll Non-saturation Fat stationary set Ramsey theory over partitions Fast club very good scale Ostaszewski square Hereditarily Lindelöf space Singular cardinals combinatorics Sierpinski's onto mapping principle stick Monotonically far Erdos Cardinal free Boolean algebra Partition Relations ZFC construction club_AD Nonspecial tree Generalized descriptive set theory Coherent tree Greatly Mahlo O-space Commutative projection system Knaster and friends Minimal Walks Chromatic number Weakly compact cardinal nonmeager set free Souslin tree Uniformly coherent Closed coloring Knaster b-scale AIM forcing weak square coloring number Sigma-Prikry polarized partition relation Dushnik-Miller Cardinal function Whitehead Problem stationary reflection Erdos-Hajnal graphs Dowker space weak Kurepa tree
Tag Archives: Postprocessing function
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
A microscopic approach to Souslin-tree constructions. Part II
Joint work with Ari Meir Brodsky. Abstract. In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known $\diamondsuit$-based constructions of Souslin trees with various additional properties may be rendered as applications of … Continue reading
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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A remark on Schimmerling’s question
Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading
The 14th International Workshop on Set Theory in Luminy, October 2017
I gave an invited talk at the 14th International Workshop on Set Theory in Luminy in Marseille, October 2017. Talk Title: Distributive Aronszajn trees Abstract: It is well-known that that the statement “all $\aleph_1$-Aronszajn trees are special” is consistent with ZFC … Continue reading
Distributive Aronszajn trees
Joint work with Ari Meir Brodsky. Abstract. Ben-David and Shelah proved that if $\lambda$ is a singular strong-limit cardinal and $2^\lambda=\lambda^+$, then $\square^*_\lambda$ entails the existence of a $\lambda$-distributive $\lambda^+$-Aronszajn tree. Here, it is proved that the same conclusion remains … Continue reading
Reflection on the coloring and chromatic numbers
Joint work with Chris Lambie-Hanson. Abstract. We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) … Continue reading
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Chang's conjecture, Chromatic number, coloring number, Fodor-type reflection, incompactness, Iterated forcing, Parameterized proxy principle, Postprocessing function, Rado's conjecture, square, stationary reflection
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