Consistency absolutely consistency there is a wff which is not a theorem consistency w.r.t negation there is no wff A such that both a and n a are theorems consistency there is a wff a such that Ty a f is absolutely consistent and consistent with respect to negation Logic in Computer Science -p6/19
Consistency absolutely consistency there is a wff which is not a theorem. consistency w.r.t negation there is no wff A such that both A and ∼ A are theorems. consistency there is a wff A such that Γ 6` A. F is absolutely consistent and consistent with respect to negation. Logic in Computer Science – p.6/19
t is consistent The following parts are equivalent fA∈C(F),then A Th(r)or N Th(T There is A E L()such that A∈Th()o~A∈Th() T is consistent Logic in Computer Science-p. 7/19
Γ is consistent The following parts are equivalent. • If A ∈ L(F), then A 6∈ Th(Γ) or ∼ A 6∈ Th(Γ) • There is A ∈ L(F) such that A 6∈ Th(Γ) or ∼ A 6∈ Th(Γ) • Γ is consistent. Logic in Computer Science – p.7/19