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Commutative projection system reflection principles Almost-disjoint family square Antichain Microscopic Approach O-space full tree Almost countably chromatic positive partition relation stick weak diamond Erdos Cardinal Erdos-Hajnal graphs Knaster xbox L-space Fat stationary set Hereditarily Lindelöf space Selective Ultrafilter Diamond-sharp square principles Uniformly homogeneous Jonsson cardinal Reduced Power Singular cofinality Fodor-type reflection Parameterized proxy principle Cardinal Invariants Open Access Diamond Nonspecial tree Ascent Path Souslin Tree Prikry-type forcing Strong coloring Successor of Regular Cardinal Sakurai's Bell inequality Respecting tree nonmeager set middle diamond Foundations Reflecting stationary set P-Ideal Dichotomy Fast club unbounded function Constructible Universe Small forcing Ulam matrix Intersection model Hindman's Theorem Successor of Singular Cardinal tensor product graph free Boolean algebra Postprocessing function sap SNR Knaster and friends S-Space projective Boolean algebra Subnormal ideal Absoluteness Strongly Luzin set Chang's conjecture OCA Cohen real higher Baire space Axiom R Was Ulam right Closed coloring Countryman line strongly bounded groups Iterated forcing Forcing Axioms weak Kurepa tree Lipschitz reduction Kurepa Hypothesis Minimal Walks stationary hitting Ineffable cardinal Dowker space very good scale Analytic sets Martin's Axiom HOD Sigma-Prikry Strongly compact cardinal Well-behaved magma Filter reflection Subadditive polarized partition relation Square-Brackets Partition Relations Rado's conjecture Chromatic number transformations Coherent tree Cardinal function Generalized descriptive set theory 54G20 Prevalent singular cardinals Diamond for trees free Souslin tree Forcing Large Cardinals Slim tree stationary reflection Hedetniemi's conjecture ZFC construction Dushnik-Miller specializable Souslin tree diamond star Local Club Condensation. Partition Relations Commutative cancellative semigroups Aronszajn tree Rock n' Roll Weakly compact cardinal ccc coloring number weak square Subtle tree property Sierpinski's onto mapping principle Mandelbrot set Almost Souslin b-scale Subtle cardinal Uniformly coherent Amenable C-sequence club_AD Club Guessing Poset regressive Souslin tree Shelah's Strong Hypothesis Uniformization Universal Sequences Non-saturation Greatly Mahlo Whitehead Problem Distributive tree AIM forcing Luzin set Singular Density Ostaszewski square C-sequence super-Souslin tree Generalized Clubs Ramsey theory over partitions Rainbow sets Vanishing levels approachability ideal incompactness Precaliber countably metacompact PFA PFA(S)[S] Singular cardinals combinatorics indecomposable ultrafilter GMA
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 $\lambda$ admits a function $\textbf{rts}:[\lambda^+]^2\rightarrow[\lambda^+]^2$ that transforms rectangles into squares. That is, whenever $A,B$ are cofinal subsets of $\lambda^+$, we have $\textbf{rts}[A\circledast B]\supseteq C\circledast C$, for some cofinal subset $C\subseteq\lambda^+$. As a … Continue reading
