definition 3.12 Biconditional

open in the book · parts/02-mathematical-methods/01-logic-sets.tex:312 · p. 20

ground object -- no derivation owed

Rests on

No declared or derived dependency edges point away from this node yet.

Supports

depends_on definition 3.17 Logical equivalence ¶
- 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 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 theorem A.17 Representability ¶ ↺
depends_on theorem 3.75 Russell, 1901 ¶

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:427
`depends_on`	←	Russell, 1901	declared	parts/02-mathematical-methods/01-logic-sets.tex:1926