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countably metacompact indecomposable ultrafilter Nonspecial tree weak Kurepa tree Diamond-sharp Diamond for trees ccc Prevalent singular cardinals regressive Souslin tree Generalized descriptive set theory Singular cofinality Aronszajn tree Ascent Path Subnormal ideal Partition Relations Erdos-Hajnal graphs PFA Whitehead Problem Coherent tree Uniformly homogeneous Reflecting stationary set Was Ulam right Uniformization Poset Strongly compact cardinal square Hereditarily Lindelöf space AIM forcing weak square Singular Density Closed coloring Well-behaved magma Dowker space Club Guessing Fodor-type reflection Axiom R Non-saturation Countryman line Square-Brackets Partition Relations Sigma-Prikry Antichain Cardinal function tensor product graph Erdos Cardinal Forcing Filter reflection b-scale Amenable C-sequence S-Space Knaster Analytic sets L-space free Boolean algebra Slim tree Souslin Tree Almost-disjoint family Selective Ultrafilter Large Cardinals incompactness Rainbow sets HOD Ineffable cardinal Sakurai's Bell inequality full tree projective Boolean algebra Postprocessing function Weakly compact cardinal Lipschitz reduction Rado's conjecture Subadditive Greatly Mahlo Fat stationary set stick Hindman's Theorem Successor of Singular Cardinal Foundations polarized partition relation specializable Souslin tree Uniformly coherent xbox Ramsey theory over partitions unbounded function Singular cardinals combinatorics Cardinal Invariants Intersection model Chromatic number positive partition relation Rock n' Roll Small forcing Chang's conjecture stationary reflection Local Club Condensation. stationary hitting approachability ideal Ostaszewski square Strongly Luzin set Vanishing levels Microscopic Approach Kurepa Hypothesis 54G20 middle diamond Mandelbrot set Ulam matrix higher Baire space Absoluteness Reduced Power Subtle cardinal Universal Sequences Open Access Luzin set Hedetniemi's conjecture Dushnik-Miller coloring number strongly bounded groups O-space Knaster and friends Distributive tree Cohen real Almost countably chromatic nonmeager set GMA very good scale diamond star club_AD Almost Souslin reflection principles Subtle tree property Generalized Clubs Minimal Walks Constructible Universe free Souslin tree ZFC construction transformations Jonsson cardinal Martin's Axiom square principles Respecting tree C-sequence Precaliber Commutative cancellative semigroups sap Commutative projection system Parameterized proxy principle Prikry-type forcing Fast club PFA(S)[S] Forcing Axioms OCA SNR Iterated forcing Successor of Regular Cardinal super-Souslin tree Sierpinski's onto mapping principle Strong coloring Diamond Shelah's Strong Hypothesis P-Ideal Dichotomy weak diamond
Tag Archives: Forcing
Same Graph, Different Universe
Abstract. May the same graph admit two different chromatic numbers in two different universes? how about infinitely many different values? and can this be achieved without changing the cardinals structure? In this paper, it is proved that in Godel’s constructible … Continue reading
Posted in Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, approachability ideal, Chromatic number, Constructible Universe, Forcing, Ostaszewski square
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INFTY Final Conference, March 2014
I gave an invited talk at the INFTY Final Conference meeting, Bonn, March 4-7, 2014. [Curiosity: Georg Cantor was born March 3, 1845] Title: Same Graph, Different Universe. Abstract: In a paper from 1998, answering a question of Hajnal, Soukup … Continue reading
Mathematics Colloquium, Bar-Ilan University, November 2013
I gave a colloquium talk at Bar-Ilan University on November 10, 2013. Title: Forcing as a tool to prove theorems Abstract: Paul Cohen celebrated solution to Hilbert’s first problem showed that the Continuum Hypothesis is independent of the usual axioms of … Continue reading
c.c.c. vs. the Knaster property
After my previous post on Mekler’s characterization of c.c.c. notions of forcing, Sam, Mike and myself discussed the value of it . We noticed that a prevalent verification of the c.c.c. goes like this: given an uncountable set of conditions, … Continue reading
