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The empty theory

  1. May 23, 2009 #1
    How do you prove the decidability of the empty theory and theory of linear orders?
     
  2. jcsd
  3. May 23, 2009 #2

    HallsofIvy

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    Uh, what is the "empty theory"?
     
  4. May 23, 2009 #3
    By empty theory I mean the theory In the empty language ( ie no non logical symbols ) with no axioms.
     
  5. May 23, 2009 #4
    The sentences of the empty theory over the empty language include only the logical connective, quantifiers and equality, so deciding them is quite simple. The empty theory over a language which includes only single-argument predicates is monadic logic, which is also decidable. The empty theory over a language which includes at least one predicate with two arguments is, however, not decidable.

    The theory of linear orders should be decidable using quantifier elimination.
     
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