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Identifier uch.math.phd//1994DIS0133
Title Υποσυστήματα του ΒΣ1+exp και κλασικά θεωρήματα της Θεωρίας Αριθμών
Alternative Title Subystems of BΣ1+exp and classical theorems of Number Theory
Creator Kornaros, Charalambos
Abstract We study provability of three theorems of elementary number theory in ΙΔo+exp and IΕ*2. We also prove, using techniques of proof theory, a known result concerning end extentions of models of ΒΣ1+exp. In chapter 1 we prove three (equivalent) statments of the prime number theorem in ΙΔo+exp. The basic step for the proof is a form of the so-called " Selberg symmetry formula". In chapter 2 we prove (a) the quadratic reciprocity law and the Selberg symmetry formula in IE*2. (b) Bertrands's postulate in N ΙΔo(π,Κ)+DEF(π)+DEF(K), where ΙΔΟ(π,Κ)+DEF(π)+DEF(K) denotes the subsystem of IE*2 obtained if we allow only two new functions symbols π,K, corresponding to the well-known functions π(χ)=number of primes<=χ, Κ(χ) = Σο <=n<=χlogn. In chapter 3 we prove, using arithmetization of the technique of tableau proofs, a theorem concerning end extensions of models of ΒΣ1+exp cofinal with ω, which was first proved by Ζ. Adamowicz by means of model-theoretic methods.
Issue date 1994-12-01
Date available 1997-06-6
Collection   School/Department--School of Sciences and Engineering--Department of Mathematics--Doctoral theses
  Type of Work--Doctoral theses
Permanent Link https://elocus.lib.uoc.gr//dlib/9/3/2/metadata-dlib-1994DIS0133.tkl Bookmark and Share
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