منابع مشابه
Infinite Hilbert Class Field Towers over Cyclotomic Fields
Weuse a result of Y. Furuta to show that for almost all positive integers m, the cyclotomic field (exp(2π i/m)) has an infinite Hilbert p-class field tower with high rankGalois groups at each step, simultaneously for all primes p of size up to about (log logm)1+o(1). We also use a recent result of B. Schmidt to show that for infinitely many m there is an infinite Hilbert p-class field tower ove...
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cement is an essential ingredient in the concrete buildings. for production of cement considerable amount of fossil fuel and electrical energy is consumed. on the other hand for generating one tone of portland cement, nearly one ton of carbon dioxide is released. it shows that 7 percent of the total released carbon dioxide in the world relates to the cement industry. considering ecological issu...
The cyclotomic polynomials
1. The definition and general results We use the notation e(t) = e 2πit. Note that e(n) = 1 for integers n, e(1 2) = −1 and e(s + t) = e(s)e(t) for all s, t. Consider the polynomial x n − 1. The complex factorisation is obvious: the zeros of the polynomial are e(k/n) for 1 ≤ k ≤ n, so x n − 1 = n k=1 x − e k n. (1) One of these factors is x − 1, and when n is even, another is x + 1. The remaini...
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In this article, we shall show that the Plotkin-Statman conjecture [?, ?] is false. The conjecture was that, in a model of the simply typed λ-calculus with only finitely many elements at each type, definability (by a closed term of the calculus) is decidable. This conjecture had been shown to imply many things, for example, Statman [?] (see also Wolfram’s book [?]) has shown it implies the deci...
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The k -provability problem is, given a first order formula φ and an integer k , to determine if φ has a proof consisting of k or fewer lines (i.e., formulas or sequents). This paper shows that the k -provability problem for the sequent calculus is undecidable. Indeed, for every r.e. set X there is a formula φ(x) and an integer k such that for all n , φ(S0) has a proof of ≤ k sequents if and onl...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05544-1