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

# Tag Archives: Constructible Universe

## 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

## Hedetniemi’s conjecture for uncountable graphs

Abstract. It is proved that in Godel’s constructible universe, for every successor cardinal $\kappa$, there exist graphs $\mathcal G$ and $\mathcal H$ of size and chromatic number $\kappa$, for which the tensor product graph $\mathcal G\times\mathcal H$ is countably chromatic. … Continue reading