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