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First order logic

  1. May 26, 2010 #1
    Let L = {f } be a first-order language containing a unary function
    symbol f , and no other non-logical symbols.
    1.Write down a sentence χ of L which is satisfiable in some structure
    with an infinite domain but is false in every structure with a finite domain.
    What can you say about the size of the domains of the models of the sentence
    2.Write down a sentence ρ such that whenever A |= ρ and A is finite,
    then A contains an even number of elements and, further, every finite set
    with an even number of elements is the domain of some model of ρ. What
    can you say about the size of the domains of the models of the sentence ¬ρ?

    Could anyone please give me some hints how to deal with this problem? I'm not sure where to start. Any help is appreciated!
     
  2. jcsd
  3. May 26, 2010 #2
    Does your definition of a first order language include the symbol "=", and is this to be interpreted as the identity in the models (i.e. are they "normal" models)?
     
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