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