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