more from Kurt Gdel

Single Idea 10611

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic]

Full Idea

The original Gdel construction gives us a sentence that a theory shows is true if and only if it satisfies the condition of being unprovable-in-that-theory.

Gist of Idea

There is a sentence which a theory can show is true iff it is unprovable

Source

report of Kurt Gdel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gdel's Theorems 20.5

Book Reference

Smith,Peter: 'An Introduction to Gdel's Theorems' [CUP 2007], p.173