List of Important Publications in Mathematics - Logic - Über Formal Unentscheidbare Sätze Der Principia Mathematica Und Verwandter Systeme, I

Über Formal Unentscheidbare Sätze Der Principia Mathematica Und Verwandter Systeme, I

(On Formally Undecidable Propositions of Principia Mathematica and Related Systems)

  • Kurt Gödel (1931)

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Description: In mathematical logic, Gödel's incompleteness theorems are two celebrated theorems proved by Kurt Gödel in 1931. The first incompleteness theorem states:

For any formal system such that (1) it is -consistent (omega-consistent), (2) it has a recursively definable set of axioms and rules of derivation, and (3) every recursive relation of natural numbers is definable in it, there exists a formula of the system such that, according to the intended interpretation of the system, it expresses a truth about natural numbers and yet it is not a theorem of the system.

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