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QuoteRef: churA_1936
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references c-d
Topic:
Turing machine
Topic:
Godel's incompleteness theorem
Topic:
limitations of formalism
Reference
Church, A., "An unsolvable problem of elementary number theory", The American Journal of Mathematics, 58, pp. 345-363, 1936. Google
Other Reference
page numbers from p. 89-107, Davis, M., The undecidable: Basic papers on undecidable propositions, undecidable problems, and computable functions, Hewlett NY: Raven Press 1965.
89 ;;Quote: Church proposed a definition for effectively calculable functions and demonstrated an unsolvable problem
90 ;;Quote: Church proposed lambda functions and recursive functions as equivalent definitions of effectively calculable. These widely different definitions support his thesis
102 ;;Quote: Church's definitions of effective calculability include algorithms and a large class of provable theorems in a system of symbolic logic
102 ;;Quote: no complete set of effectively calculable invariants of conversion exist; for example, if Principia Mathematica is omega-consistent, its Enthscheidungsproblem is unsolvable
ThesaHelp: references c-d (337 items)
Topic: Turing machine (30 items)
Topic: Godel's incompleteness theorem (19 items)
Topic: limitations of formalism (92 items)