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