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### 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

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

# 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