### 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

Universal Sequences Absoluteness Partition Relations free Boolean algebra Poset OCA Antichain Martin's Axiom Successor of Regular Cardinal Whitehead Problem Chang's conjecture square Large Cardinals ccc Kurepa Hypothesis Club Guessing 05A17 Parameterized proxy principle xbox projective Boolean algebra Hindman's Theorem Fast club Foundations L-space Forcing Axioms Microscopic Approach Non-saturation Jonsson cardinal Fat stationary set Prikry-type forcing Ascent Path Singular coﬁnality incompactness Erdos Cardinal PFA(S)[S] Rainbow sets weak square Uniformization Cardinal Invariants stationary hitting Fodor-type reflection weak diamond Square-Brackets Partition Relations Diamond polarized partition relation 20M14 Mandelbrot set Cohen real Axiom R diamond star Constructible Universe Rado's conjecture Almost-disjoint famiy Souslin Tree sap Reduced Power Singular Density Almost countably chromatic Slim tree middle diamond Ostaszewski square Selective Ultrafilter Aronszajn tree HOD Almost Souslin Knaster 05D10 reflection principles Coherent tree Minimal Walks Chromatic number Stevo Todorcevic Shelah's Strong Hypothesis Singular cardinals combinatorics Hedetniemi's conjecture coloring number Cardinal function square principles Sakurai's Bell inequality approachability ideal b-scale P-Ideal Dichotomy Small forcing Successor of Singular Cardinal Forcing Dushnik-Miller Commutative cancellative semigroups stationary reflection Erdos-Hajnal graphs very good scale Hereditarily Lindelöf space Singular Cofinality Rock n' Roll S-Space Prevalent singular cardinals Weakly compact cardinal 11P99 tensor product graph PFA Generalized Clubs

# 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