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