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Math Help - V-sentence

  1. #1
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    V-sentence

    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.
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  2. #2
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    Could you say what a V-sentence is?
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  3. #3
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    Let V be a vocabulary. A V-formula is a formula in which every
    function, relation, and constant is in V. A V-sentence is a V-formula that is a
    sentence.
    example about it the V-sentence ∀y∃x(1+xx = y).
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  4. #4
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    @Mike12
    It appears to me, that you are using some sort of highly specialized text material.
    It seems to involve both graph theory and formal logic.
    I think that you need to be more detailed in writing up the questions.
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  5. #5
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    the question is to define a a V-sentence phi such that phi has arbitrarily large finite models and , for any finite model G , |G| is even . and then find a finite graph G such that |G| is even and G doesnot model the sentence phi .
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  6. #6
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    Let V be a vocabulary. A V-formula is a formula in which every
    function, relation, and constant is in V.
    And what is the vocabulary V in this particular problem? If V is completely arbitrary, then what is the goal of emphasizing that \phi 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 \phi. This means that V must have relations and/or functions to talk about graphs, so V is not completely arbitrary.

    Edit: Maybe "a person from a country" is not a good example. I mean, "from a nation" rather than "not from a city".
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