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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

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

# Tag Archives: 05C63

## 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