Archives
Keywords
Closed coloring Chang's conjecture Greatly Mahlo Subadditive free Souslin tree Hindman's Theorem Successor of Singular Cardinal Rainbow sets Erdos-Hajnal graphs Sakurai's Bell inequality diamond star Singular cardinals combinatorics L-space reflection principles Precaliber Dowker space Hereditarily Lindelöf space incompactness Fat stationary set Diamond-sharp Almost Souslin super-Souslin tree very good scale Aronszajn tree Iterated forcing Small forcing Nonspecial tree Amenable C-sequence Slim tree Open Access O-space Hedetniemi's conjecture Knaster and friends Subnormal ideal Mandelbrot set Partition Relations Strongly Luzin set stationary hitting Diamond Diamond for trees Cardinal Invariants Analytic sets OCA xbox stationary reflection Was Ulam right? stick Universal Sequences positive partition relation unbounded function weak Kurepa tree 54G20 Vanishing levels C-sequence Shelah's Strong Hypothesis Singular Density Fast club Jonsson cardinal middle diamond AIM forcing PFA Uniformization Uniformly coherent Distributive tree Souslin Tree P-Ideal Dichotomy Prikry-type forcing Luzin set Weakly compact cardinal full tree approachability ideal indecomposable ultrafilter Microscopic Approach Generalized descriptive set theory Subtle cardinal Absoluteness Foundations Club Guessing Ineffable cardinal ZFC construction Erdos Cardinal PFA(S)[S] sap nonmeager set ccc HOD Strong coloring Parameterized proxy principle Countryman line Axiom R Forcing Axioms Almost countably chromatic Generalized Clubs Rock n' Roll square principles Uniformly homogeneous club_AD Martin's Axiom Minimal Walks Coherent tree Knaster Rado's conjecture Forcing Ulam matrix regressive Souslin tree Ramsey theory over partitions free Boolean algebra Large Cardinals specializable Souslin tree Ostaszewski square Reflecting stationary set Dushnik-Miller Local Club Condensation. Fodor-type reflection Cohen real Constructible Universe Reduced Power Sierpinski's onto mapping principle Lipschitz reduction Singular cofinality GMA Prevalent singular cardinals Commutative projection system Kurepa Hypothesis Antichain b-scale Successor of Regular Cardinal Cardinal function Almost-disjoint family Postprocessing function Chromatic number Subtle tree property Ascent Path Non-saturation square Filter reflection countably metacompact coloring number tensor product graph Well-behaved magma Poset S-Space Strongly compact cardinal weak square Sigma-Prikry SNR higher Baire space projective Boolean algebra Selective Ultrafilter Intersection model Square-Brackets Partition Relations Commutative cancellative semigroups transformations strongly bounded groups Respecting tree polarized partition relation weak diamond Whitehead Problem
Tag Archives: stationary reflection
Knaster and friends II: The C-sequence number
Joint work with Chris Lambie-Hanson. Abstract. Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable … Continue reading
The 15th International Workshop on Set Theory in Luminy, September 2019
I gave an invited talk at the 15th International Workshop on Set Theory in Luminy in Marseille, September 2019. Talk Title: Chain conditions, unbounded colorings and the C-sequence spectrum. Abstract: The productivity of the
Posted in Invited Talks
Tagged Closed coloring, Knaster, Precaliber, stationary reflection, unbounded function
Comments Off on The 15th International Workshop on Set Theory in Luminy, September 2019
Knaster and friends I: Closed colorings and precalibers
Joint work with Chris Lambie-Hanson. Abstract. The productivity of the
A remark on Schimmerling’s question
Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether
Weak square and stationary reflection
Joint work with Gunter Fuchs. Abstract. It is well-known that the square principle
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, stationary reflection, weak square
Leave a comment
MFO workshop in Set Theory, February 2017
I gave an invited talk at the Set Theory workshop in Obwerwolfach, February 2017. Talk Title: Coloring vs. Chromatic. Abstract: In a joint work with Chris Lambie-Hanson, we study the interaction between compactness for the chromatic number (of graphs) and … Continue reading
Posted in Invited Talks
Tagged Chromatic number, coloring number, incompactness, stationary reflection
Leave a comment
The eightfold way
Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. Three central combinatorial properties in set theory are the tree property, the approachability property and stationary reflection. We prove the mutual independence of these properties by showing … 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
The reflection principle
A few years ago, in this paper, I introduced the following reflection principle: Definition.
Posted in Blog
Tagged reflection principles, square, stationary reflection, Weakly compact cardinal
Leave a comment
Young Researchers in Set Theory, March 2011
These are the slides of a talk I gave at the Young Researchers in Set Theory 2011 meeting (Königswinter, 21–25 March 2011). Talk Title: Around Jensen’s square principle Abstract: Jensen‘s square principle for a cardinal
