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Diamond-sharp Filter reflection Hindman's Theorem Iterated forcing Subnormal ideal Diamond for trees Erdos-Hajnal graphs Club Guessing transformations Ostaszewski square Singular cardinals combinatorics Local Club Condensation. Cardinal Invariants Slim tree polarized partition relation diamond star PFA incompactness approachability ideal Almost-disjoint family Strongly compact cardinal Successor of Regular Cardinal Rado's conjecture Sigma-Prikry Forcing Axioms Sierpinski's onto mapping principle weak square Commutative projection system specializable Souslin tree unbounded function club_AD stationary hitting Generalized descriptive set theory super-Souslin tree Uniformly homogeneous Universal Sequences Singular Density HOD Partition Relations Dowker space full tree countably metacompact Foundations Subtle tree property Non-saturation Strong coloring Weakly compact cardinal Fat stationary set tensor product graph Successor of Singular Cardinal Whitehead Problem Parameterized proxy principle Constructible Universe Prikry-type forcing Chang's conjecture Selective Ultrafilter ccc Ascent Path square very good scale strongly bounded groups Commutative cancellative semigroups Microscopic Approach projective Boolean algebra Fast club regressive Souslin tree PFA(S)[S] S-Space Countryman line Analytic sets Lipschitz reduction Diamond Vanishing levels Erdos Cardinal Almost countably chromatic Absoluteness Minimal Walks P-Ideal Dichotomy Strongly Luzin set SNR Distributive tree Poset O-space xbox Rock n' Roll Small forcing Almost Souslin reflection principles Shelah's Strong Hypothesis C-sequence Was Ulam right? Dushnik-Miller Rainbow sets Singular cofinality Respecting tree Reflecting stationary set sap Large Cardinals Ulam matrix OCA free Souslin tree Forcing weak diamond Well-behaved magma Ineffable cardinal Cardinal function ZFC construction Fodor-type reflection stick Souslin Tree indecomposable ultrafilter Square-Brackets Partition Relations Uniformization Coherent tree Greatly Mahlo Chromatic number Axiom R L-space Hereditarily Lindelöf space Luzin set coloring number Martin's Axiom Subadditive Uniformly coherent Jonsson cardinal Postprocessing function Ramsey theory over partitions stationary reflection nonmeager set Subtle cardinal Hedetniemi's conjecture Amenable C-sequence 54G20 square principles Generalized Clubs Prevalent singular cardinals b-scale weak Kurepa tree Sakurai's Bell inequality Kurepa Hypothesis Cohen real GMA Knaster Mandelbrot set middle diamond Intersection model Nonspecial tree Closed coloring higher Baire space Aronszajn tree Antichain Open Access free Boolean algebra AIM forcing Reduced Power Knaster and friends Precaliber positive partition relation
Category Archives: Publications
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
Strong failures of higher analogs of Hindman’s Theorem
Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
1 Comment
More notions of forcing add a Souslin tree
Joint work with Ari Meir Brodsky. Abstract. An
Ordinal definable subsets of singular cardinals
Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. A remarkable result by Shelah states that if
Higher Souslin trees and the GCH, revisited
Abstract. It is proved that for every uncountable cardinal
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, Open Access, regressive Souslin tree, Souslin Tree, square, Weakly compact cardinal, xbox
16 Comments
A microscopic approach to Souslin-tree constructions. Part I
Joint work with Ari Meir Brodsky. Abstract. We propose a parameterized proxy principle from which
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E65, 05C05, Coherent tree, Diamond, Microscopic Approach, Parameterized proxy principle, Slim tree, Souslin Tree, square, xbox
5 Comments
Square with built-in diamond-plus
Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, Respecting tree, square, xbox
1 Comment
Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a
Putting a diamond inside the square
Abstract. By a 35-year-old theorem of Shelah,
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Diamond, square, Successor of Singular Cardinal
1 Comment
