definition 3.17 Logical equivalence

open in the book · parts/02-mathematical-methods/01-logic-sets.tex:422 · p. 21

Rests on

depends_on proposition 3.19 Conditional as disjunction ¶
- depends_on proposition 3.21 Contraposition ¶
depends_on proposition 3.20 De Morgan's laws ¶
depends_on proposition 3.22 Algebra of propositions ¶
- 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.30 Church, Turing ¶
      - depends_on theorem A.26 Diagonal lemma ¶
      - depends_on theorem A.27 Rosser ¶
  - depends_on theorem A.17 Representability ¶ ↺

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Biconditional	declared	parts/02-mathematical-methods/01-logic-sets.tex:427
`depends_on`	→	Tautology	declared	parts/02-mathematical-methods/01-logic-sets.tex:427
`depends_on`	←	Conditional as disjunction	declared	parts/02-mathematical-methods/01-logic-sets.tex:447
`depends_on`	←	De Morgan's laws	declared	parts/02-mathematical-methods/01-logic-sets.tex:482
`depends_on`	←	Algebra of propositions	declared	parts/02-mathematical-methods/01-logic-sets.tex:561