### 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

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

# 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