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ZFC construction higher Baire space Selective Ultrafilter 54G20 Hereditarily Lindelöf space Poset Small forcing Cardinal function Ascent Path ccc Reflecting stationary set stationary reflection Kurepa Hypothesis Distributive tree Postprocessing function Lipschitz reduction Microscopic Approach Shelah's Strong Hypothesis Dowker space Rado's conjecture very good scale projective Boolean algebra Diamond-sharp Constructible Universe Fat stationary set HOD Minimal Walks Analytic sets full tree Cardinal Invariants Foundations Hedetniemi's conjecture Subtle cardinal Uniformly coherent Prikry-type forcing regressive Souslin tree free Boolean algebra Sigma-Prikry PFA(S)[S] Successor of Regular Cardinal club_AD Coherent tree Weakly compact cardinal Dushnik-Miller Universal Sequences polarized partition relation Rainbow sets PFA super-Souslin tree Club Guessing transformations Nonspecial tree L-space Open Access Jonsson cardinal O-space Partition Relations C-sequence Hindman's Theorem Was Ulam right Mandelbrot set Square-Brackets Partition Relations weak diamond Greatly Mahlo Uniformization free Souslin tree weak square tensor product graph Singular cofinality Ulam matrix sap stick stationary hitting Closed coloring Luzin set GMA weak Kurepa tree Precaliber reflection principles Commutative cancellative semigroups b-scale Aronszajn tree Well-behaved magma Iterated forcing Local Club Condensation. Vanishing levels indecomposable ultrafilter incompactness Successor of Singular Cardinal coloring number Subnormal ideal square Almost-disjoint family Reduced Power Fast club Ineffable cardinal Filter reflection Fodor-type reflection Erdos Cardinal strongly bounded groups OCA Almost Souslin Absoluteness Singular Density S-Space Forcing Axioms Ramsey theory over partitions Erdos-Hajnal graphs positive partition relation Almost countably chromatic Ostaszewski square Uniformly homogeneous Subadditive Amenable C-sequence nonmeager set Rock n' Roll Whitehead Problem square principles countably metacompact Parameterized proxy principle Singular cardinals combinatorics diamond star Prevalent singular cardinals Diamond unbounded function Strongly Luzin set Slim tree xbox Martin's Axiom Diamond for trees Non-saturation Sierpinski's onto mapping principle Cohen real Souslin Tree P-Ideal Dichotomy Forcing middle diamond Chang's conjecture Chromatic number Knaster specializable Souslin tree SNR approachability ideal Antichain Generalized Clubs Axiom R Knaster and friends Generalized descriptive set theory Large Cardinals AIM forcing Strong coloring Subtle tree property Sakurai's Bell inequality
Blog Archives
Partitioning the club guessing
In a recent paper, I am making use of the following fact. Theorem (Shelah, 1997). Suppose that $\kappa$ is an accessible cardinal (i.e., there exists a cardinal $\theta<\kappa$ such that $2^\theta\ge\kappa)$. Then there exists a sequence $\langle g_\delta:C_\delta\rightarrow\omega\mid \delta\in E^{\kappa^+}_\kappa\rangle$ … Continue reading
Erdős 100
The influential mathematician Paul Erdős was born 100 years ago, 26 March 1913, in Budapest. One evidence of his impact on mathematics is reflected in the particular list of invited speakers for the upcoming conference in his honor. Erdős is also … Continue reading
Infinite Combinatorics Seminar, Haifa University, June, 2012
I gave a talk at the University of Haifa on June 07, 2012, intended for general audience. Title: Strong Colorings: the study of the failure of generalized Ramsey statements Abstract: A strong coloring from $X$ to $Y$ is a function … Continue reading
Posted in Contributed Talks
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The chromatic numbers of the Erdos-Hajnal graphs
Recall that a coloring $c:G\rightarrow\kappa$ of an (undirected) graph $(G,E)$ is said to be chromatic if $c(v_1)\neq c(v_2)$ whenever $\{v_1,v_2\}\in E$. Then, the chromatic number of a graph $(G,E)$ is the least cardinal $\kappa$ for which there exists a chromatic … Continue reading
Posted in Blog, Expository
Tagged Chromatic number, Erdos-Hajnal graphs, Rado's conjecture, reflection principles
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Comparing rectangles with squares through rainbow sets
In Todorcevic’s class last week, he proved all the results of Chapter 8 from his Walks on Ordinals book, up to (and including) Theorem 8.1.11. The upshots are as follows: Every regular infinite cardinal $\theta$ admits a naturally defined function … Continue reading
A large cardinal in the constructible universe
In this post, we shall provide a proof of Silver’s theorem that the Erdos caridnal $\kappa(\omega)$ relativizes to Godel’s constructible universe. First, recall some definitions. Given a function $f:[\kappa]^{<\omega}\rightarrow \mu$, we say that $I\subseteq\kappa$ is a set of indiscernibles for … Continue reading
