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