theorem A.27 Rosser

open in the book · appendices/A-long-proofs.tex:2425 · p. 2804

Rests on

depends_on lemma A.19 Numerals behave ¶
- 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 A.118 eq:app-inc-Q-successor ¶
- depends_on equation A.119 eq:app-inc-order ¶
- proves proof app:A-long-proofs@proof-13 ¶
depends_on theorem A.26 Diagonal lemma ¶
- depends_on proposition A.15 Syntax is computable ¶
  - depends_on definition 3.93 Computable function, decidable set ¶
    - depends_on definition 3.92 Turing machine ¶
  - depends_on definition 3.81 Effective axiomatization ¶
    - depends_on definition 3.80 Formal system ¶ ↺
  - depends_on equation A.120 eq:app-inc-coding ¶
  - proves proof app:A-long-proofs@proof-12 ¶
- depends_on theorem A.17 Representability ¶
  - depends_on definition A.16 Representability ¶
    - depends_on definition 3.80 Formal system ¶ ↺
  - depends_on definition 3.93 Computable function, decidable set ¶ ↺
  - depends_on lemma A.20 $\Sigma_{1}$-completeness ¶
    - depends_on definition A.18 $\Delta_{0}$ and $\Sigma_{1}$ ¶
      - depends_on equation A.119 eq:app-inc-order ¶ ↺
    - depends_on lemma A.19 Numerals behave ¶ ↺
    - depends_on proposition 3.22 Algebra of propositions ¶
      - depends_on definition 3.17 Logical equivalence ¶
      - depends_on definition 3.6 Truth table ¶
      - proves proof ch:01-logic-sets@proof-4 ¶
    - proves proof app:A-long-proofs@proof-14 ¶
  - depends_on theorem A.25 thm:app-inc-primrec ¶
    - depends_on definition A.16 Representability ¶ ↺
    - depends_on lemma A.23 Sequence lemma ¶
      - depends_on definition A.22 Gödel's $\beta$ ¶
      - depends_on lemma A.21 Chinese remainder theorem ¶
      - proves proof app:A-long-proofs@proof-16 ¶
    - depends_on lemma A.24 lem:app-inc-beta-delta0 ¶
      - depends_on definition A.22 Gödel's $\beta$ ¶ ↺
      - depends_on definition A.18 $\Delta_{0}$ and $\Sigma_{1}$ ¶ ↺
      - depends_on lemma A.19 Numerals behave ¶ ↺
      - proves proof app:A-long-proofs@proof-17 ¶
    - depends_on lemma A.19 Numerals behave ¶ ↺
    - depends_on lemma A.20 $\Sigma_{1}$-completeness ¶ ↺
    - proves proof app:A-long-proofs@proof-18 ¶
  - proves proof app:A-long-proofs@proof-19 ¶
- proves proof app:A-long-proofs@proof-20 ¶
depends_on theorem A.17 Representability ¶ ↺
proves proof app:A-long-proofs@proof-21 ¶

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Edges

type	direction	node	provenance	where
`depends_on`	→	Numerals behave	declared	appendices/A-long-proofs.tex:2428
`depends_on`	→	Diagonal lemma	declared	appendices/A-long-proofs.tex:2428
`depends_on`	→	Representability	declared	appendices/A-long-proofs.tex:2428
`proves`	←	app:A-long-proofs@proof-21	declared	appendices/A-long-proofs.tex:2431