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### 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

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

# Category Archives: Infinite Graphs

## 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
10 Comments

## 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

## Chromatic numbers of graphs – large gaps

Abstract. We say that a graph $G$ is $(\aleph_0,\kappa)$-chromatic if $\text{Chr}(G)=\kappa$, while $\text{Chr}(G’)\le\aleph_0$ for any subgraph $G’$ of $G$ of size $<|G|$. The main result of this paper reads as follows. If $\square_\lambda+\text{CH}_\lambda$ holds for a given uncountable cardinal $\lambda$, … Continue reading

Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Almost countably chromatic, Chromatic number, incompactness, Ostaszewski square
6 Comments