Using Ehrenfeucht-Fraisse show that there is no set of first order formulas.
We consider class of all graphs (finite and finite). We would like to show that it is not possible to axiomatize in first logic that: nodes may be coloured with finite number of colors in such way that each triple has different colors.
I can show it using compactness theorem, but I must use Ehrenfeucht-Fraisse game. I know that we should show that for each $n\in\mathbb{N}$ there are exists two graphs such that one of them satisfy this sentence and second not satisfy and, whats vitally, duplicator always may win in game with $n$ stages.