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Suppose $\sigma$ is a vocabulary consisting of one binary relation $E$ and let $\phi$ be a $\sigma$ sentence. Is it decidable whether there is a finite directed graph $G$, with all in- and out-degrees $0$ or $1$, such that $G\models \phi$ ?

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    $\begingroup$ This is a very elementary question, and not of the level usually answered here. Read any basic text on Finite Model Theory and you should know the answer. $\endgroup$ – Marc Hamann Mar 10 '13 at 15:44
  • $\begingroup$ Welcome to cstheory, a Q&A site for research-level questions in theoretical computer science (TCS). Your question does not appear to be a research-level question in TCS. Please see the FAQ for more information on what is meant by this. Your question might be suitable for Computer Science which has a broader scope. $\endgroup$ – Kaveh Mar 11 '13 at 4:48

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