theorem 3.88 Gödel's second incompleteness theorem

open in the book · parts/02-mathematical-methods/01-logic-sets.tex:2525 · p. 48

Rests on

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 equation 3.90 eq:con-sentence ¶
depends_on theorem 3.87 Gödel, 1931 ¶
- 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 definition 3.80 Formal system ¶ ↺
  - proves proof ch:01-logic-sets@prooflink-3 ¶
- proves proof ch:01-logic-sets@proof-20 ¶
proves proof ch:01-logic-sets@proof-21 ¶

Nothing declares a dependency on this node yet.

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:2534
`depends_on`	→	Peano arithmetic	declared	parts/02-mathematical-methods/01-logic-sets.tex:2535
`depends_on`	→	eq:con-sentence	declared	parts/02-mathematical-methods/01-logic-sets.tex:2535
`depends_on`	→	Gödel, 1931	declared	parts/02-mathematical-methods/01-logic-sets.tex:2535
`proves`	←	ch:01-logic-sets@proof-21	declared	parts/02-mathematical-methods/01-logic-sets.tex:2538