**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

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