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)

Online version: Online version

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.

Read more about this topic:  List Of Important Publications In Mathematics, Logic

Famous quotes containing the words der and/or formal:

    Under the lindens on the heather,
    There was our double resting-place.
    —Walther Von Der Vogelweide (1170?–1230?)

    Good gentlemen, look fresh and merrily.
    Let not our looks put on our purposes,
    But bear it as our Roman actors do,
    With untired spirits and formal constancy.
    William Shakespeare (1564–1616)