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