definition 3.82 Consistency, completeness, soundness

open in the book · parts/02-mathematical-methods/01-logic-sets.tex:2320 · p. 45

Rests on

depends_on definition A.5 Maximal consistent ¶
- depends_on definition A.9 The term structure ¶
  - depends_on lemma A.11 Truth lemma ¶
    - depends_on theorem A.12 Model existence ¶
      - depends_on corollary A.14 Compactness ¶
      - depends_on theorem A.13 Completeness ¶
  - depends_on lemma A.10 lem:app-comp-welldefined ¶
    - depends_on lemma A.11 Truth lemma ¶ ↺
  - depends_on theorem A.12 Model existence ¶ ↺
- depends_on lemma A.6 Lindenbaum ¶
- depends_on lemma A.7 Behaviour of a maximal consistent set ¶
  - depends_on lemma A.11 Truth lemma ¶ ↺
  - depends_on lemma A.10 lem:app-comp-welldefined ¶ ↺
depends_on lemma A.8 Adding witnesses preserves consistency ¶
- depends_on lemma A.11 Truth lemma ¶ ↺
depends_on theorem 3.84 Gödel's completeness theorem, 1930 ¶
- depends_on theorem A.30 Church, Turing ¶
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 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Formal system	declared	parts/02-mathematical-methods/01-logic-sets.tex:2334
`depends_on`	→	Negation	declared	parts/02-mathematical-methods/01-logic-sets.tex:2334
`depends_on`	←	Maximal consistent	declared	appendices/A-long-proofs.tex:1555
`depends_on`	←	Adding witnesses preserves consistency	declared	appendices/A-long-proofs.tex:1657
`depends_on`	←	Gödel's completeness theorem, 1930	declared	parts/02-mathematical-methods/01-logic-sets.tex:2386
`depends_on`	←	Gödel, 1931	declared	parts/02-mathematical-methods/01-logic-sets.tex:2471
`depends_on`	←	Tarski's undefinability of truth	declared	parts/02-mathematical-methods/01-logic-sets.tex:2639