### 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
- Genearlizations 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

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

# 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