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