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