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By Roland Barthes

The Rustle of Language is a suite of forty-five essays, written among 1967 and 1980, on language, literature, and teaching--the excitement of the text--in an authoritative translation by means of Richard Howard.

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A) Let JA = JB - {B} if B t B = Bt (b) Let JA = lB - (c) Let JA = JB B or B2 ~ JB and otherwise let JA = JB B 2• {B} if B t B= - V eJ e lB and B2 ~ JB and otherwise let JA = JB • Bt~B2' {B} if B t E JB and B2 e lB and otherwise let JA = JB • INTRODUCING HPC 35 (d) No atomic wff are in I and so the atomic case does not arise. The reader can verify that if A < B then fA:J fB and if A E fA then A E fB for all B. n LEMMA. AEI fA = 1. Proof. The proof is by induction on the length of the proof of wff in 1.

A) IIA(x), ... , x n )lIr = 1 iff the set {s I(g(x\), ... , g(xn =1 »E D(s, A)} iff IIAllr = 1 and IIBlir = 1. (b) IIA (c) IIfllr = 1 iff (d) IIVxA(x)lIr = 1 iff for all A Bllr "A(x)"f' = 1. bars t, for A atomic. N bars t. g' = xg 48 CHAPTER 3 (e) "A ~ Bllf = then (f) (g) 1 iff for all s, if tRs and IIBII~ = 1. IIA v Bllf = 1 iff {s /IIAII~ = 1 or IIAII~ = 1 IIBII~ = 1} bars t. 113xA(x)"f = 1 iff {s /there exists a g' = xg with IIA(x)II~' = 1} bars t. We say that A holds (or is valid) in the structure under g iff IIAllfJ = 1.

If Bn = VxB(x), then for some u, an IfttD en, B(u) (by property (*)) so let a n+1 = an. e n+1 = en U {B(u)} U {VxB(x)}. Case 2. an l~tD en, B n, if Bn is not existential, let a n+1 = an U {Bn}, e n+1 = en. (~n+h e n+1) is clearly l~tD consistent, since (an, en) is. If Bn = 3xB(x), then by property (*), since an, Bn lff-tD en. for some u, an, B(u) lH-tD en. so let a n+1 = {B(u), Bn} U an, e n+1 = en. Thus (a n+ h e n +1) is defined, is consistent and has (*). Let a = U n ~n' e = Un en, then (~, e) is the desired extension.

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