Graph ›
Arithmetization and the Incompleteness Theorems
Arithmetization and the Incompleteness Theorems
foundations results equations depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) definition A5.2: Representability A5.2 Representability definition A5.4: \Delta_0 and \Sigma_1 A5.4 \Delta_0 and \Si… definition A5.8: Gödel's \beta A5.8 Gödel's \beta proposition A5.1: Syntax is computable A5.1 Syntax is comput… theorem A5.3: Representability A5.3 Representability lemma A5.5: Numerals behave A5.5 Numerals behave lemma A5.6: \Sigma_1-completeness A5.6 \Sigma_1-complet… lemma A5.7: Chinese remainder theorem A5.7 Chinese remainde… lemma A5.9: Sequence lemma A5.9 Sequence lemma lemma A5.10: lem:app-inc-beta-delta0 A5.10 lemma theorem A5.11: thm:app-inc-primrec A5.11 theorem theorem A5.12: Diagonal lemma A5.12 Diagonal lemma theorem A5.13: Rosser A5.13 Rosser proposition A5.14: prop:app-inc-derivability A5.14 proposition theorem A5.15: Second incompleteness theorem A5.15 Second incomplet… theorem A5.16: Church, Turing A5.16 Church, Turing equation A5.1: eq:app-inc-Q-successor eq. (A5.1) equation A5.2: eq:app-inc-order eq. (A5.2) equation A5.3: eq:app-inc-coding eq. (A5.3) equation A5.12: eq:app-inc-prov eq. (A5.12) The chain of Arithmetization and the Incompleteness Theorems: 20 of 20 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.