Gödel (1931) Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I
- Schema.org Type:
ScholarlyArticle - Authors: Kurt Gödel
- Year / Venue: 1931 — Monatshefte für Mathematik und Physik, 38, 173-198
- URL: https://doi.org/10.1007/BF01700692
gist
十分な算術的強度と実効性を持つ無矛盾な形式体系には決定不能命題が存在し、体系自身の無矛盾性を内部で証明できないことを示した古典論文
Verbatim Quotes
- Theorem VI & XI, pp. 187-196:
“For every ω-consistent recursive class κ of formulae there are recursive class-signs r, such that neither v Gen r nor Neg(v Gen r) belongs to Flg(κ)… and a formal system cannot prove its own consistency.”