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Completeness of finite first order theories

  1. Mar 24, 2009 #1
    Is every first order theory with finitely many axioms automatically complete? An axiom schema like that of ZFC's separation counts as an infinite number of axioms.
     
  2. jcsd
  3. Mar 24, 2009 #2
    Nevermind. Robinson arithmetic is a counterexample.
     
  4. Mar 25, 2009 #3
    The empty theory over a non-empty language is the trivial counter-example.
     
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