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weak diamond Erdos Cardinal Ostaszewski square Erdos-Hajnal graphs Reflecting stationary set very good scale Well-behaved magma Ascent Path Uniformly homogeneous 54G20 Hindman's Theorem Forcing Axioms Axiom R Local Club Condensation. Hereditarily Lindelöf space free Souslin tree specializable Souslin tree ccc Square-Brackets Partition Relations Martin's Axiom stationary reflection Mandelbrot set Kurepa Hypothesis Uniformization Precaliber Club Guessing ZFC construction Non-saturation coloring number reflection principles super-Souslin tree Chang's conjecture Singular cardinals combinatorics Sierpinski's onto mapping principle Iterated forcing Rado's conjecture Parameterized proxy principle Souslin Tree Subadditive Singular cofinality L-space GMA Coherent tree Absoluteness Universal Sequences Hedetniemi's conjecture Rock n' Roll Lipschitz reduction AIM forcing Vanishing levels Knaster Amenable C-sequence OCA Countryman line Luzin set unbounded function Whitehead Problem Prikry-type forcing Strong coloring Subnormal ideal strongly bounded groups Open Access Poset Commutative projection system S-Space Dushnik-Miller sap stick Diamond Nonspecial tree Distributive tree Forcing Knaster and friends PFA(S)[S] middle diamond Filter reflection Small forcing Slim tree Singular Density Aronszajn tree Fast club Almost-disjoint family Fat stationary set free Boolean algebra weak square club_AD Analytic sets Ramsey theory over partitions Jonsson cardinal Selective Ultrafilter Partition Relations Fodor-type reflection PFA Foundations Rainbow sets Subtle cardinal C-sequence Sakurai's Bell inequality SNR approachability ideal Ineffable cardinal Subtle tree property regressive Souslin tree Large Cardinals Antichain higher Baire space Strongly Luzin set indecomposable ultrafilter polarized partition relation Successor of Singular Cardinal Cardinal function Successor of Regular Cardinal xbox Shelah's Strong Hypothesis Almost Souslin Reduced Power Was Ulam right? weak Kurepa tree HOD Generalized descriptive set theory Sigma-Prikry square Respecting tree Generalized Clubs Chromatic number Dowker space Microscopic Approach Diamond for trees Constructible Universe O-space Minimal Walks Closed coloring Cohen real stationary hitting b-scale Cardinal Invariants full tree Strongly compact cardinal Intersection model transformations projective Boolean algebra P-Ideal Dichotomy Weakly compact cardinal countably metacompact Prevalent singular cardinals nonmeager set diamond star Greatly Mahlo Uniformly coherent Almost countably chromatic incompactness Postprocessing function square principles tensor product graph Diamond-sharp positive partition relation Ulam matrix Commutative cancellative semigroups
Tag Archives: Square-Brackets Partition Relations
Sums of triples in Abelian groups
Joint work with Ido Feldman. Abstract. Motivated by a problem in additive Ramsey theory, we extend Todorcevic’s partitions of three-dimensional combinatorial cubes to handle additional three-dimensional objects. As a corollary, we get that if the continuum hypothesis fails, then for … Continue reading
Strongest transformations
Joint work with Jing Zhang. Abstract. We continue our study of maps transforming high-dimensional complicated objects into squares of stationary sets. Previously, we proved that many such transformations exist in ZFC, and here we address the consistency of the strongest … Continue reading
Posted in Partition Relations, Publications
Tagged Diamond, Minimal Walks, square, Square-Brackets Partition Relations, stick, transformations, xbox
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Transformations of the transfinite plane
Joint work with Jing Zhang. Abstract. We study the existence of transformations of the transfinite plane that allow one to reduce Ramsey-theoretic statements concerning uncountable Abelian groups into classical partition relations for uncountable cardinals. To exemplify: we prove that for every … Continue reading
6th European Set Theory Conference, July 2017
I gave a 3-lecture tutorial at the 6th European Set Theory Conference in Budapest, July 2017. Title: Strong colorings and their applications. Abstract. Consider the following questions. Is the product of two
Posted in Invited Talks, Open Problems
Tagged b-scale, Cohen real, Luzin set, Minimal Walks, Souslin Tree, Square-Brackets Partition Relations
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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
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Prolific Souslin trees
In a paper from 1971, Erdos and Hajnal asked whether (assuming CH) every coloring witnessing
Posted in Blog, Expository
Tagged Rainbow sets, Souslin Tree, Square-Brackets Partition Relations
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Complicated colorings
Abstract. If
Posted in Partition Relations, Publications
Tagged Minimal Walks, Open Access, Square-Brackets Partition Relations
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MFO workshop in Set Theory, January 2014
I gave an invited talk at the Set Theory workshop in Obwerwolfach, January 2014. Talk Title: Complicated Colorings. Abstract: If
Rectangular square-bracket operation for successor of regular cardinals
Joint work with Stevo Todorcevic. Extended Abstract: Consider the coloring statement
Comparing rectangles with squares through rainbow sets
In Todorcevic’s class last week, he proved all the results of Chapter 8 from his Walks on Ordinals book, up to (and including) Theorem 8.1.11. The upshots are as follows: Every regular infinite cardinal
