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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

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

# Tag Archives: 05C15

## Reflection on the coloring and chromatic numbers

Joint work with Chris Lambie-Hanson. Abstract. We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) … Continue reading

## 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