An Unsolvable Problem of Elementary Number Theory.

Church, A. (1936). An Unsolvable Problem of Elementary Number Theory. American Journal of Mathematics, 58(2), 345-363.

Type

Journal article

Intellectual base

Primary research

Year

1936

Volume

58

Issue

2

Pages

345-363

DOI

10.2307/2371045

DOI registrant

JSTOR

Link

https://doi.org/10.2307/2371045

Cited from

computer_science, mathematics, philosophy

Cited by

4 citations across 4 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Decidability Computability
  • Add multiplication and the same syntax yields Peano arithmetic, whose theoremhood is undecidable: by Church's theorem no uniform terminating procedure settles provability for the whole class.

    This sourceEstablishes the undecidability of first-order arithmetic (Church's theorem), so theoremhood in Peano arithmetic admits no decision procedure.

• Deductive Reasoning

  • This sourceProposes effective calculability via lambda-definability and proves an unsolvable problem of number theory (Church's theorem). WebSearch confirmed venue, pages, DOI, and lambda-calculus content.

• Function (Mapping)
  • Lambda calculus

Domain-specific

• Applicative programming language
  • … language is organized primarily around value-level expressions in which functions are applied to arguments, inheriting the application and beta-reduction perspective of lambda calculus; the label overlaps substantially with functional language but excludes function composition alone as a sufficient identity.

Verification

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