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16 Jul 2008: Ψ′ =(. 0 λxnbλxnb 0 A. AT Ψ. )for some 0 6= λ k, b R and A Mat2,n2(R). ... So (4.3) becomes. (4.4) A(xng h)T = (λxn b)(f2f1. )for some linear form b R.

13 Aug 2008: a,b,c), (a′,b,c′). for some b. Corollary 2.3 Let (a0,c0), (a1,b1),. , ... As we explain in Section 4 this leads us to hope that wecan in some sense borrow an exponential from the relationalmodel.

20 Jan 2008: 7) Let R be a commutative ring with unit. For a,b R we say that a divides b (notation a|b) ifb = ac for some c R. ... If R is a domain, then a b (a|b b|a). We call an elementa RR irreducible if for any factorization a = bc one of b,c is a unit

21 Aug 2008: iii) there is a generic object G 2 E. P. for some distinguished object P 2 B,. ... i) P =? =) (P! Q) = U. Suppose there are some a; b 2 U for which ab is undened and.

20 Feb 2008: 1.6. Some special cases. We next show that the rank of αi attains the upperbound given in Theorem B in some special cases. ... Hence there exists h H suchthat xh := h1xh = ya for some a > 1.

21 Aug 2008: ForestForest. of A of BFigure 1: The forest of questions of A ) B.At any stage of a play, not every move is necessarilyavailable to the players; however some moves may ... Suppose at some point afterinteracting with the environment, the name a has been in

21 Aug 2008: iii) there is a generic object G 2 E. P. for some distinguished object P 2 B,. ... i) P =? =) (P! Q) = U. Suppose there are some a; b 2 U for which ab is undened and.

8 Jan 2008: However, the work we have already done enables us to produce some niceinfinite dimensional Banach spaces. ... For historical reasons Baire’s theorem is associated with some rather un-helpful nomenclature.

19 Aug 2008: def. (〈a〉, 〈〉. ), S. (ι2(b). )=def. (〈〉, 〈b〉. )for a A and b B. ... We introduce some abbreviations for future reference. For x P(A B),we write (x.1, x.2) for S](x), so that we have x.1 PA and x.2

18 Aug 2008: A B) (C D)are not equal. (There are some similar issues for the triangle diagrams.). ... V andW for a conjunction and disjunction according to some bracketings.In these circumstances we say thatiA;B, i>, iC;D and i?