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