### Archives

### Recent blog posts

- 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
- Partitioning the club guessing January 22, 2014

### Keywords

stationary hitting weak diamond square Ostaszewski square Square-Brackets Partition Relations HOD Ascent Path Non-saturation PFA Small forcing Reduced Power L-space Cardinal Invariants square principles reflection principles Hedetniemi's conjecture Parameterized proxy principle free Boolean algebra Stevo Todorcevic Jonsson cardinal Forcing Foundations Mandelbrot set polarized partition relation Distributive tree xbox Shelah's Strong Hypothesis Antichain Chang's conjecture Almost Souslin Microscopic Approach 05A17 Aronszajn tree Fodor-type reflection P-Ideal Dichotomy Selective Ultrafilter Singular Density Rock n' Roll Whitehead Problem approachability ideal Fat stationary set Slim tree Hereditarily Lindelöf space Forcing Axioms Kurepa Hypothesis Fast club projective Boolean algebra Commutative cancellative semigroups stationary reflection Constructible Universe Erdos-Hajnal graphs tensor product graph Martin's Axiom Absoluteness Singular cardinals combinatorics Dushnik-Miller Club Guessing Almost countably chromatic Sakurai's Bell inequality OCA ccc Minimal Walks 20M14 Knaster Successor of Singular Cardinal Uniformization Rainbow sets Uniformly coherent Axiom R Singular coﬁnality Successor of Regular Cardinal middle diamond sap diamond star incompactness super-Souslin tree Cohen real S-Space very good scale Prikry-type forcing weak square b-scale Coherent tree Prevalent singular cardinals Poset Rado's conjecture Chromatic number Souslin Tree Partition Relations Cardinal function Almost-disjoint famiy Erdos Cardinal Universal Sequences Weakly compact cardinal coloring number Hindman's Theorem PFA(S)[S] Postprocessing function Luzin set Generalized Clubs Diamond Large Cardinals 11P99 Nonspecial 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