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29 Mar 2011: affordsus no variables (as it might be ‘F’ and ‘G’) to range over the second orderobjects captured by the branching quantifiers which would enable us to say‘F = G’. ... 8). Let us instantiate ‘u’ for the lower-case variables in (8)

16 Aug 2011: C =X CX , the union in each case ranging over all permissible values of X. ... Why does the proof of Lemma 1 not carry over? Suppose, say, we performthe compression C123,45 on A, and B A is intersecting.

25 Aug 2011: Clearly we must have|B| = n 1. Now Theorem 3 tells us that B contains the maximal numberof intersecting pairs over all families in [n](2) of size n 1. ... We see that I is the disjoint union of the sets IB over all collections B of2-sets in A.

16 Oct 2011: We work over a perfect field K with characteristic not equal to 2, 3 or 5. ... where the sums are taken over all cyclic permutations of the subscripts mod 5.The models u(a,b), called the Hesse models, are representative of all genus onemodels in the

9 May 2011: ζ,a), (ξ,b)〉 = ζbξa. Given an elliptic curve E over K we define XE(n) to be XM in the case M isE[n] equipped with the Weil pairing. ... functions in c4(A,B) and c6(A,B), thereby giving the formulae in Theorem 1.1.The following alternative proof of

29 Jul 2011: We consider smooth representations of G over an algebraicallyclosed field C of characteristic zero. ... qj(1j)/2JS. #J=j. aJ. αa. as S ranges over subsets of {1,.

18 Jul 2011: It will alsobe true for the generic elliptic curve y2 = x3 ax b over Q(a, b). ... Proof: Let v1 = 1, v2, v3, v4 be a basis for L+ over K.

12 Jul 2011: 2.1) Definition. Let V be a finite-dimensional vector space over F. ... 2.11) Given G,V over F of dimension n and ρ : G GL(V ). Fixa basis B for V ; we get a linear isomorphism φ : V F n, v 7