Could you say what a V-sentence is?
can we define a V-sentence phi such that phi has arbitrarily large finite models and , for any finite model G , |G| is even . and then finding a finite graph G such that |G| is even and G doesnot model the sentence phi that I mentioned above.
please explain it to me.
And what is the vocabulary V in this particular problem? If V is completely arbitrary, then what is the goal of emphasizing that must only use V? Every formula is in some vocabulary. This is similar to saying, "Find a person from a country": every person is from some country. Also, later you are talking about a graph that is or is not a model of . This means that V must have relations and/or functions to talk about graphs, so V is not completely arbitrary.Let V be a vocabulary. A V-formula is a formula in which every
function, relation, and constant is in V.
Edit: Maybe "a person from a country" is not a good example. I mean, "from a nation" rather than "not from a city".