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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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