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

# 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