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19 Dec 2014: if B = {min(Xα) : α < κ} is stationary.(iii) If {Xα : α < κ} is pairwise disjoint, then there exists a [κ]κ such that. ... Prove that there exists a family F of2κ stationary subsets of S such that if A 6= B F , then A B and B A arestationary in

19 Dec 2014: i) Prove that 20 = 1 implies the following assertion SD :there exist sets A and B such that R2 = AB and Al and Bm are countablefor every horizontal line l and ... exist x1 and x2 such that x1 6 f(x2) and x2 6 f(x1).

18 Sep 2014: Variables, such as x, y, z, a, b, c, or finite tuples of variables: x = (x1,. , ... is true then there exists a homomorphism η : GΣ Mi such that the diagramGΣ.

18 Sep 2014: To see this, choose δ such that, for x anend-point of a base b, d(x, bo S) δ. ... Let c b bean interval with end-point x such that c0 S =. Choose δ depending on Kaccording to the previous claim, and let y, k K be such that:.

2 Dec 2014: If ϕ AutK(L) where L = K(t), show that there exist a, b, c, d K withad 6= bc such that ϕ(t) = (at b)/(ct d), and conversely that ... a) such that f splits over L = Q(. a)( 3α).

16 Jul 2014: Mark Gross Mirror symmetry and the SYZ conjecture. Definition. A tropical affine manifold with singularities is a real (C 0) manifoldB along with an open subset B0 B such that := B ... For each integral point v of a two-face, we can choose anopen

18 Sep 2014: Thence it also extends to M̃. Since M is compact there exists positive such that for all p M, B(p)is ball-like (homeomorphic to a ball in Tp(M) ... 19. Proof: By the definition of the connected sum, there exists an embedded 2-sphere F in M such that M F

14 Oct 2014: 8. Let A1, A2, A3,. be sets such that A1 A2. ... c there is an x with a < x < b such that f(x) = c.

3 Feb 2014: Show that for any b C, there exists a sequence of points zn Ba(r) withzn 6= a such that zn a and f(zn) b as n. ... Find such a sequence when f(z) = e1/z, a = 0 and b = 2.

19 Dec 2014: Let M be a CTM such that (T is an ever-branching Suslin tree )M. ... λ < κ. Prove that if | A |= κ and x Aimplies | x |< λ, then there exists B A such that | B |= κ and (r)(x B)(x 6=y xy = r).

18 Jul 2014: such that if Φ X5(K) is non-singular then CΦ has Jacobian. ... We define an action. of GL5 GL5 on the space of such matrices via.

2 Jan 2014: Hyland. existence of such a situation Lambek and Scott exploit an elegant categorical reduc-. ... for a theory in the language of the pure λ-calculus: such a theory corresponds to a.

14 Jan 2014: Show that T can be written Tz = Az Bz̄for unique A,B C. ... Can such a map be therestriction to the strip of a Möbius map?

18 Sep 2014: Proof. Let C be such that the Γ-translates of B(x0,C) cover X. ... BecauseB is compact, there is an > 0 such that Bp() is CAT(0) for every p B.

20 Oct 2014: such as this. (1) The condition about the number of quadruples a b = c d can be interpreted as. ... Then there exist sets A X and B Y of density α and β such thatη(A,B) αβδ(1 c).

15 Apr 2014: 37 ζ. 57 ζ. 67 ) =. 7. Definition 3.4. An invariant of degree m is a homogeneous polynomial I =. I(a,b,c) of degree m such that I g = I ... variables a,b,c such that v g = gv, respectively v g = gT v, for all g G.

1 Feb 2014: In dealing with chains of reasoning such as A = B, B = C,. ... A drawback of such a development would be that Jape would no longerembrace forms of logic that don’t fit DAGs.

26 Nov 2014: If A is the matrix of the first of these (say), find a non-singular matrix P such that PTAP is diagonalwith entries 1. ... 14. Let a1, a2,. , an be real numbers such that a1 an = 0 and a21 a2n = 1.

13 Oct 2014: tion for lattices of such small determinant is typically infeasible. 8 WATKINS, DONNELLY, ELKIES, FISHER, GRANVILLE & ROGERS. ... For instance, Rubinstein [51, (1.15)] reports the biasfor various curves in terms of such an integrated quantity.

26 Nov 2014: 2) Let K be a field containing an n-th primitive root of unity for some n > 1.Let a,b K such that the polynomials f(t) = tn a and ... Rn = R such that R1 is 1-step constructible from S, andfor each 1 i n 1, Ri1 is 1-step constructible from S {R1,.