Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $G=(V,E)$ be a directed graph. Let $E$ be a binary relation such that $(x,y) \in E$ iff there is an edge from vertex $x$ to vertex $y$.

Let the world of first order interpretation be the set of vertices. A vertex cover $C \subseteq V $ of a graph $G=(V,E)$ is a set such that

$$(x,y) \in E \Rightarrow x \in C \lor y \in C.$$

How would I prove that the set of all first order interpretations that have a finite vertex cover is not definable.

Thanks in advance.

share|improve this question
    
Try using Ehrenfeucht–Fraïssé game. I'm trying to figure it out, too. –  joachim Jan 20 '13 at 11:11

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.