### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014

### Keywords

Chromatic number Almost-disjoint famiy Constructible Universe very good scale Square-Brackets Partition Relations Distributive tree Almost countably chromatic Generalized Clubs weak square Luzin set Cardinal function Axiom R Antichain Weakly compact cardinal Sakurai's Bell inequality Erdos-Hajnal graphs Singular cardinals combinatorics Chang's conjecture Martin's Axiom Large Cardinals Singular coﬁnality Jonsson cardinal Uniformly coherent PFA(S)[S] b-scale Rock n' Roll P-Ideal Dichotomy Souslin Tree Fast club Almost Souslin Hedetniemi's conjecture Rainbow sets Hindman's Theorem Club Guessing Postprocessing function Microscopic Approach incompactness Selective Ultrafilter stationary hitting polarized partition relation Erdos Cardinal Commutative cancellative semigroups PFA Slim tree Minimal Walks Whitehead Problem middle diamond Ostaszewski square S-Space Prikry-type forcing super-Souslin tree ccc Stevo Todorcevic weak diamond HOD Foundations reflection principles xbox Mandelbrot set stationary reflection Prevalent singular cardinals Successor of Singular Cardinal Coherent tree Non-saturation square principles Fodor-type reflection Dushnik-Miller Small forcing Knaster Aronszajn tree Hereditarily Lindelöf space Parameterized proxy principle Kurepa Hypothesis Absoluteness coloring number approachability ideal free Souslin tree diamond star OCA Shelah's Strong Hypothesis Uniformization Poset Fat stationary set Universal Sequences square L-space Successor of Regular Cardinal sap Rado's conjecture Forcing Partition Relations Cohen real Diamond Ascent Path free Boolean algebra Reduced Power projective Boolean algebra specializable Souslin tree Nonspecial tree Singular Density Forcing Axioms tensor product graph Cardinal Invariants

# 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