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