definition 3.83 Peano arithmetic

open in the book · parts/02-mathematical-methods/01-logic-sets.tex:2344 · p. 45

Rests on

depends_on lemma A.19 Numerals behave ¶
- depends_on lemma A.24 lem:app-inc-beta-delta0 ¶
  - depends_on theorem A.25 thm:app-inc-primrec ¶
    - depends_on theorem A.17 Representability ¶
      - depends_on proposition A.28 prop:app-inc-derivability ¶
      - depends_on theorem A.30 Church, Turing ¶
      - depends_on theorem A.26 Diagonal lemma ¶
      - depends_on theorem A.27 Rosser ¶
- depends_on lemma A.20 $\Sigma_{1}$-completeness ¶
  - depends_on theorem A.25 thm:app-inc-primrec ¶ ↺
  - depends_on theorem A.17 Representability ¶ ↺
- depends_on theorem A.25 thm:app-inc-primrec ¶ ↺
- depends_on theorem A.27 Rosser ¶ ↺
depends_on lemma 3.86 Diagonal lemma ¶
- depends_on theorem 3.87 Gödel, 1931 ¶
  - depends_on theorem A.29 Second incompleteness theorem ¶
  - depends_on theorem 3.88 Gödel's second incompleteness theorem ¶
- depends_on theorem 3.91 Tarski's undefinability of truth ¶
depends_on theorem 3.88 Gödel's second incompleteness theorem ¶ ↺

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Peano axioms	declared	parts/02-mathematical-methods/01-logic-sets.tex:2361
`depends_on`	→	Principle of induction	declared	parts/02-mathematical-methods/01-logic-sets.tex:2361
`depends_on`	→	Formal system	declared	parts/02-mathematical-methods/01-logic-sets.tex:2361
`depends_on`	←	Numerals behave	declared	appendices/A-long-proofs.tex:2059
`depends_on`	←	Diagonal lemma	declared	parts/02-mathematical-methods/01-logic-sets.tex:2444
`depends_on`	←	Gödel's second incompleteness theorem	declared	parts/02-mathematical-methods/01-logic-sets.tex:2535