### 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

Reduced Power Almost-disjoint famiy PFA(S)[S] Coherent tree approachability ideal Weakly compact cardinal Large Cardinals Microscopic Approach Antichain Prevalent singular cardinals Fat stationary set Chang's conjecture middle diamond Dushnik-Miller Minimal Walks stationary hitting Aronszajn tree Singular coﬁnality Rock n' Roll Poset Selective Ultrafilter Cardinal Invariants Small forcing Forcing Axioms Fast club very good scale Mandelbrot set Stevo Todorcevic OCA 11P99 Uniformly coherent Sakurai's Bell inequality projective Boolean algebra Rado's conjecture Uniformization Successor of Singular Cardinal Forcing Whitehead Problem S-Space b-scale Club Guessing diamond star Commutative cancellative semigroups Almost Souslin Hedetniemi's conjecture Singular Density super-Souslin tree coloring number Erdos-Hajnal graphs Hindman's Theorem Ostaszewski square Shelah's Strong Hypothesis HOD Generalized Clubs weak square L-space sap free Boolean algebra Erdos Cardinal Parameterized proxy principle incompactness reflection principles square principles weak diamond Cardinal function Universal Sequences Square-Brackets Partition Relations Slim tree Axiom R Almost countably chromatic stationary reflection PFA Rainbow sets Diamond Knaster Souslin Tree ccc Nonspecial tree Jonsson cardinal square 05A17 Luzin set Foundations Non-saturation Successor of Regular Cardinal Postprocessing function Chromatic number polarized partition relation Hereditarily Lindelöf space free Souslin tree tensor product graph Cohen real Martin's Axiom Prikry-type forcing Partition Relations Constructible Universe xbox Kurepa Hypothesis Fodor-type reflection specializable Souslin tree Ascent Path Absoluteness Singular cardinals combinatorics P-Ideal Dichotomy Distributive tree

# 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
10 Comments

## 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