theorem 3.87 Gödel, 1931

open in the book · parts/02-mathematical-methods/01-logic-sets.tex:2460 · p. 47

Rests on

depends_on definition 3.82 Consistency, completeness, soundness ¶
- depends_on definition 3.80 Formal system ¶
- depends_on definition 3.7 Negation ¶
depends_on definition 3.81 Effective axiomatization ¶
- depends_on definition 3.80 Formal system ¶ ↺
depends_on equation 3.86 eq:provability-predicate ¶
depends_on lemma 3.86 Diagonal lemma ¶
- depends_on definition 3.83 Peano arithmetic ¶
  - depends_on axiom 3.33 Peano axioms ¶
  - depends_on axiom 3.34 Principle of induction ¶
  - depends_on definition 3.80 Formal system ¶ ↺
- depends_on definition 3.80 Formal system ¶ ↺
- proves proof ch:01-logic-sets@prooflink-3 ¶
proves proof ch:01-logic-sets@proof-20 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`cites`	→	Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I	derived	parts/02-mathematical-methods/01-logic-sets.tex:2470
`cites`	→	Extensions of Some Theorems of Gödel and Church	derived	parts/02-mathematical-methods/01-logic-sets.tex:2470
`depends_on`	→	Consistency, completeness, soundness	declared	parts/02-mathematical-methods/01-logic-sets.tex:2471
`depends_on`	→	Effective axiomatization	declared	parts/02-mathematical-methods/01-logic-sets.tex:2471
`depends_on`	→	eq:provability-predicate	declared	parts/02-mathematical-methods/01-logic-sets.tex:2471
`depends_on`	→	Diagonal lemma	declared	parts/02-mathematical-methods/01-logic-sets.tex:2471
`depends_on`	←	Second incompleteness theorem	declared	appendices/A-long-proofs.tex:2513
`depends_on`	←	Gödel's second incompleteness theorem	declared	parts/02-mathematical-methods/01-logic-sets.tex:2535
`proves`	←	ch:01-logic-sets@proof-20	declared	parts/02-mathematical-methods/01-logic-sets.tex:2474