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13 Aug 2008: logical operations.Such subcollections arise naturally when the PCA (A, ) has some additionalstructure respected by application. ... An extensional assembly is an object (X, | = |) of the topos S[PER] such that.

29 Sep 2008: 2-natural in C such that the diagram. [C,D]kB- [[B,C], [B,D]]. kA- [[A, [B,C]], [A, [B,D]]]. ... Note that what wecall pseudo-maps [3] call morphisms.) We write f = (f, f̄) : A B for such apseudo-map, the 2-cell usually being understood.

20 Jan 2008: b) Let N Zn be a submodule of rank n. Show that there is a matrix A Mn(Z) such thatA(Zn) = N and the index [Zn : N] of N in ... 8) An integral domain R is called a euclidian domain if there is a map N : R{0} Z>0 such thatfor all a,b R, b 6= 0, there are

2 Dec 2008: Does there exist such a bijection f which isorder-preserving (that is, satisfies f(x) < f(y) whenever x < y)? ... Let S be a collection of subsets of N such that for every A, B S we have eitherA B or B A.

27 Aug 2008: Wecan dene a procedure called normalisation which can systematically eliminate such de-tours from a deduction. ... Much work has been done on providing such (categorical) models ofIntuitionistic Linear Logic.

27 Aug 2008: Wecan dene a procedure called normalisation which can systematically eliminate such de-tours from a deduction. ... Much work has been done on providing such (categorical) models ofIntuitionistic Linear Logic.

13 Aug 2008: Thus concretely maps A B of Dial(I) consist of maps f : I U V andF : I U Y X in T such that α(i,u,F(i,u,y)) ... or equivalently. (f,F) : (U X•) V U• Y •. such that an entailment which I write. (

20 Feb 2008: Assume there is θ OK such that 1, θ,. , θn1 is anintegral basis of OK. ... dK| (. nn. n! )2 ( π4. )n. Deduce that |dK| > 1 for every number field K 6= Q.(b) Show that there are constants A > 1, c > 1, such that for every

28 Nov 2008: Then there exists a basis B for V such that. [ψ]B =. . 0 11 0 0. 0 11 0 0. 0 0 1. ... For each α End(V ) there exists a unique α End(V ) such that.

13 May 2008: A language L over vocabulary W is a set of strings, such that L W. ... input. A string is rejected only if there is no such sequence.