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- 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

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

# 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