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