Extensions of Some Theorems of Gödel and Church

  title={Extensions of Some Theorems of G{\"o}del and Church},
  author={J. Barkley Rosser},
  journal={J. Symb. Log.},
  • J. Rosser
  • Published 1936
  • Mathematics, Computer Science
  • J. Symb. Log.
We shall say that a logic is “simply consistent” if there is no formula A such that both A and ∼ A are provable. “ω-consistent” will be used in the sense of Godel. “General recursive” and “primitive recursive” will be used in the sense of Kleene, so that what Godel calls “rekursiv” will be called “primitive recursive.” By an “ Entscheidungsverfahren ” will be meant a general recursive function ϕ ( n ) such that, if n is the Godel number of a provable formula, ϕ ( n ) = 0 and, if n is not the… Expand

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