### 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

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

# 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