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  1. Algebraic Extensions in Nonstandard Models and Hilbert's Irreducibility Theorem.Masahiro Yasumoto - 1988 - Journal of Symbolic Logic 53 (2):470-480.
    LetKbe an algebraic number field andIKthe ring of algebraic integers inK. *Kand *IKdenote enlargements ofKandIKrespectively. LetxЄ *K–K. In this paper, we are concerned with algebraic extensions ofKwithin *K. For eachxЄ *K–Kand each natural numberd, YKis defined to be the number of algebraic extensions ofKof degreedwithin *K.xЄ *K–Kis called a Hilbertian element ifYK= 0 for alldЄ N,d> 1; in other words,Khas no algebraic extension within *K. In their paper [2], P. C. Gilmore and A. Robinson proved that the existence of a (...)
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  2.  20
    Forcing on Bounded Arithmetic II.Gaisi Takeuti & Masahiro Yasumoto - 1998 - Journal of Symbolic Logic 63 (3):860-868.
  3.  4
    Nonstandard Arithmetic of Hilbert Subsets.Masahiro Yasumoto - 1991 - Annals of Pure and Applied Logic 52 (1-2):195-202.
    Let f ϵ Z [ X, Y ] be irreducible. We give a condition that there are only finitely many integers n ϵ Z such that f is reducible and we give a bound for such integers. We prove a similar result for polynomials with coefficients in polynomial rings. Both results are proved by, so-called, nonstandard arithmetic.
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  4.  13
    Separations of First and Second Order Theories in Bounded Arithmetic.Masahiro Yasumoto - 2005 - Archive for Mathematical Logic 44 (6):685-688.
    We prove that PTCN cannot be a model of U12. This implies that there exists a first order sentence of bounded arithmetic which is provable in U12 but does not hold in PTCN.
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  5. Forcing on Bounded Arithmetic II.Gaisi Takeuti & Masahiro Yasumoto - 1998 - Journal of Symbolic Logic 63 (3):860-868.
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