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Ramsey theory over partitions Rock n' Roll Dowker space ccc Almost countably chromatic Generalized Clubs C-sequence Fodor-type reflection positive partition relation Reflecting stationary set full tree square Rado's conjecture Selective Ultrafilter regressive Souslin tree Amenable C-sequence club_AD S-Space Jonsson cardinal Slim tree Luzin set indecomposable filter Local Club Condensation. PFA(S)[S] Square-Brackets Partition Relations xbox incompactness Reduced Power Sakurai's Bell inequality Well-behaved magma transformations L-space Entangled linear order Monotonically far very good scale Kurepa Hypothesis Hindman's Theorem OCA HOD Forcing Axioms Parameterized proxy principle reflection principles Forcing with side conditions Chang's conjecture Interval topology on trees middle diamond Generalized descriptive set theory Constructible Universe Poset Forcing Axiom R Cohen real Diamond-sharp 54G20 approachability ideal Weakly compact cardinal Distributive tree Partition relations for trees super-Souslin tree Closed coloring Precaliber Vanishing levels Strong coloring diamond star Fast club square principles Cardinal function Uniformization Commutative projection system Filter reflection Partition Relations Commutative cancellative semigroups Uniformly homogeneous Universal Sequences Analytic sets GMA stick strongly bounded groups specializable Souslin tree P-Ideal Dichotomy countably metacompact nonmeager set ZFC construction stationary reflection Minimal Walks Subnormal ideal Singular cofinality Ostaszewski square Sigma-Prikry Ulam matrix Lipschitz reduction Chromatic number O-space Was Ulam right? unbounded function weak square Coherent tree free Boolean algebra Ineffable cardinal Strongly Luzin set Sierpinski's onto mapping principle Ascending path Subadditive Successor of Singular Cardinal Nonspecial tree Prevalent singular cardinals Open Access PFA Microscopic Approach Absoluteness Postprocessing function coloring number Whitehead Problem polarized partition relation Strongly compact cardinal Cardinal Invariants Knaster and friends AIM forcing Fat stationary set weak diamond Singular cardinals combinatorics Singular Density Antichain Subtle cardinal stationary hitting Souslin Tree Small forcing higher Baire space Ascent Path perfectly normal weak Kurepa tree Club Guessing Non-saturation Dushnik-Miller Aronszajn tree Greatly Mahlo Hedetniemi's conjecture Respecting tree Erdos Cardinal Mandelbrot set Shelah's Strong Hypothesis Rainbow sets Erdos-Hajnal graphs Uniformly coherent Hereditarily Lindelöf space Subtle tree property tensor product graph Diamond for trees Successor of Regular Cardinal Foundations Intersection model Countryman line Almost Souslin Prikry-type forcing sap free Souslin tree Diamond SNR b-scale Almost-disjoint family projective Boolean algebra Knaster Large Cardinals Iterated forcing Martin's Axiom
Tag Archives: Square-Brackets Partition Relations
Dushnik-Miller for regular cardinals (part 2)
In this post, we shall provide a proof of Todorcevic’s theorem, that $\mathfrak b=\omega_1$ implies $\omega_1\not\rightarrow(\omega_1,\omega+2)^2$. This will show that the Erdos-Rado theorem that we discussed in an earlier post, is consistently optimal. Our exposition of Todorcevic’s theorem would be … Continue reading
CMS Winter Meeting, December 2011
I gave an invited special session talk at the 2011 meeting of the Canadian Mathematical Society. Talk Title: The extent of the failure of Ramsey’s theorem at successor cardinals. Abstract: We shall discuss the results of the following papers: Transforming … Continue reading
Posted in Invited Talks
Tagged Square-Brackets Partition Relations
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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
