An informal exposition of proofs of Gödel's theorems and Church's theorem

  title={An informal exposition of proofs of G{\"o}del's theorems and Church's theorem},
  author={J. Barkley Rosser},
  journal={Journal of Symbolic Logic},
  pages={53 - 60}
  • J. Rosser
  • Published 1 June 1939
  • Philosophy, Mathematics
  • Journal of Symbolic Logic
This paper is an attempt to explain as non-technically as possible the principles and devices used in the various proofs of Gödel's Theorems and Church's Theorem. Roman numerals in references shall refer to the papers in the bibliography. In the statements of Gödel's Theorems and Church's Theorem, we will employ the phrase “for suitable L.” The hidden assumptions which we denote by this phrase have never been put down explicitly in a form intelligible to the average reader. The necessity for… 

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  • J. Rosser
  • Mathematics, Philosophy
    Journal of Symbolic Logic
  • 1936
It is proved that simple consistency implies the existence of undecidable propositions and the non-existence of an Entscheidungsverfahren by a strengthening of Godel's Satz VI and Kleene's Theorem XIII.

An Unsolvable Problem of Elementary Number Theory

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Tm ( I)T function and is defined by an integer m. Let F express "m defines a general recursive function

    If L is ^-consistent and if the formula expressing "Bew(x)" is provable, then "Bew(x)

      A less difficult exposition of Godel's work is to be found in Carnap's The logical syntax of language

      • Ober formal unentscheidbare S&tze der Principia Mathematica und verwandter Sysleme I, Monatshefte fiir Mathematik und Physik
      • 1931

      By an extensive argument involving "rekursiv" functions, Godel shows that for a large class of L's: (c)