Archives
Keywords
Subadditive Martin's Axiom SNR Nonspecial tree positive partition relation Partition Relations HOD Local Club Condensation. b-scale Erdos Cardinal Intersection model Hindman's Theorem square principles Uniformly homogeneous Non-saturation Strong coloring Analytic sets Ostaszewski square PFA diamond star Ramsey theory over partitions Fat stationary set OCA very good scale Subtle tree property projective Boolean algebra Interval topology on trees specializable Souslin tree Weakly compact cardinal Almost-disjoint family transformations Countryman line Successor of Singular Cardinal Successor of Regular Cardinal Square-Brackets Partition Relations Coherent tree weak Kurepa tree Sierpinski's onto mapping principle Uniformly coherent Lipschitz reduction Vanishing levels Generalized Clubs Diamond for trees Ascending path Parameterized proxy principle L-space Respecting tree strongly bounded groups regressive Souslin tree Whitehead Problem perfectly normal super-Souslin tree Dushnik-Miller Small forcing ZFC construction Mandelbrot set nonmeager set stick Closed coloring Rock n' Roll Entangled linear order Subtle cardinal Forcing Axioms free Souslin tree coloring number tensor product graph square P-Ideal Dichotomy 54G20 Antichain Kurepa Hypothesis Amenable C-sequence Postprocessing function Microscopic Approach Fast club Absoluteness Chromatic number Reduced Power Knaster and friends full tree Strongly compact cardinal Rado's conjecture Was Ulam right? middle diamond Precaliber Dowker space C-sequence Strongly Luzin set Almost Souslin Universal Sequences Subnormal ideal Well-behaved magma Rainbow sets Reflecting stationary set Constructible Universe Cardinal function Cardinal Invariants GMA Hereditarily Lindelöf space polarized partition relation stationary hitting Ineffable cardinal Commutative projection system Club Guessing stationary reflection Prevalent singular cardinals approachability ideal Forcing with side conditions Large Cardinals countably metacompact Sakurai's Bell inequality PFA(S)[S] reflection principles Generalized descriptive set theory indecomposable filter Axiom R Ascent Path Slim tree Foundations Singular cofinality Sigma-Prikry Knaster Jonsson cardinal Commutative cancellative semigroups weak diamond AIM forcing Souslin Tree sap Forcing Iterated forcing Chang's conjecture unbounded function Open Access Minimal Walks Diamond club_AD ccc Ulam matrix Greatly Mahlo Shelah's Strong Hypothesis Hedetniemi's conjecture Aronszajn tree Uniformization Diamond-sharp Almost countably chromatic Singular cardinals combinatorics Distributive tree free Boolean algebra Poset O-space Fodor-type reflection Luzin set Cohen real Singular Density Partition relations for trees weak square xbox higher Baire space Monotonically far Filter reflection incompactness Erdos-Hajnal graphs S-Space Prikry-type forcing Selective Ultrafilter
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
Comments Off on CMS Winter Meeting, December 2011
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
