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