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I defend the following version of the ought-implies-can principle: (OIC) by virtue of conceptual necessity, an agent at a given time has an (objective, pro tanto) obligation to do only what the agent at that time has the ability and opportunity to do. In short, obligations correspond to ability plus opportunity. My argument has three premises: (1)(More)
The historical development of Hensel’s lemma is briefly discussed (section 1). Using Newton polygons, a simple proof of a general Hensel’s lemma for separable polynomials over Henselian fields is given (section 3). For polynomials over algebraically closed, valued fields, best possible results on continuity of roots (section 4) and continuity of factors(More)
It is investigated when a cyclic p-class field of an imaginary quadratic number field can be embedded in an infinite pro-cyclic p-extension. Résumé. On donne des conditions pour qu’un p-corps de classes cyclique d’un corps de nombres quadratique imaginaire soit plongeable dans une p-extension pro-cyclique infinie. Consider an imaginary quadratic number(More)
It is a theorem of Kaplansky that a prime p ≡ 1 (mod 16) is representable by both or none of x2 + 32y2 and x2 + 64y2, whereas a prime p ≡ 9 (mod 16) is representable by exactly one of these binary quadratic forms. In this paper five similar theorems are proved. As an example, one theorem states that a prime p ≡ 1 (mod 20) is representable by both or none of(More)
The demandingness of act consequentialism (AC) is well-known and has received much sophisticated treatment.1 Few have been content to defend AC’s demands. Much of the response has been to jettison AC in favor of a similar, though significantly less demanding view.2 The popularity of this response is easy to understand. Excessive demandingness appears to be(More)
The minimal number of spheres (without “interior”) of radius n required to cover the finite set {0, . . . , q−1} equipped with the Hamming distance is denoted by T (n, q). The only hitherto known values of T (n, q) are T (n, 3) for n = 1, . . . , 6. These were all given in the 1950s in the Finnish football pool magazine Veikkaaja along with upper and lower(More)
with coefficients aij in O. Write the degree as k = pm with p m. A solution x = (x1, . . . , xN) ∈ K is called non-trivial if at least one xj is non-zero. It is a special case of a conjecture of Emil Artin that (∗) has a non-trivial solution whenever N > Rk. This conjecture has been verified by Davenport and Lewis for a single diagonal equation over Qp and(More)