proposition 3.22 Algebra of propositions

open in the book · parts/02-mathematical-methods/01-logic-sets.tex:540 · p. 23

Rests on

depends_on definition 3.17 Logical equivalence ¶
- depends_on definition 3.12 Biconditional ¶
- depends_on definition 3.14 Tautology ¶
depends_on definition 3.6 Truth table ¶
proves proof ch:01-logic-sets@proof-4 ¶

Supports

depends_on lemma A.7 Behaviour of a maximal consistent set ¶
- 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 lemma A.20 $\Sigma_{1}$-completeness ¶
- 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.29 Second incompleteness theorem ¶
    - depends_on theorem A.30 Church, Turing ¶
    - depends_on theorem A.26 Diagonal lemma ¶
      - depends_on theorem A.27 Rosser ¶
    - depends_on theorem A.27 Rosser ¶ ↺
- depends_on theorem A.17 Representability ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Logical equivalence	declared	parts/02-mathematical-methods/01-logic-sets.tex:561
`depends_on`	→	Truth table	declared	parts/02-mathematical-methods/01-logic-sets.tex:561
`depends_on`	←	Behaviour of a maximal consistent set	declared	appendices/A-long-proofs.tex:1612
`depends_on`	←	$\Sigma_{1}$-completeness	declared	appendices/A-long-proofs.tex:2110
`proves`	←	ch:01-logic-sets@proof-4	declared	parts/02-mathematical-methods/01-logic-sets.tex:564