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Sets of degrees of computable fields
 Elie Bienenstock
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Given a Σ_{2} (resp. Σ_{1}) degree of recursive unsolvability a, a computable field (resp. a computable field with a splitting algorithm)F is constructed in any given characteristic, such that the set of dimensions of all finite extensions ofF has degree a.
This is part of an M.Sc. Thesis presented at The Hebrew University. The author wishes to express his indebtedness to his Supervisor Professor H. Gaifman for his constant guidance and encouragement. Thanks are also due to Professor G. Sabbagh (University of Paris VII) for several useful suggestions.
 Ax, J. (1968) The elementary theory of finite fields. Ann. of Math. 88: pp. 239271 CrossRef
 Bourbaki, N. (1950) Algèbre. Hermann, Paris
 Ershov, Ju. L. (1973) Constructive models, inSelected Questions of Algebra and Logic. Nauka, Novosibirsk
 Gordon, Basil, Straus, E. G. (1965) On the degrees of the finite extensions of a field. Proc. Symp. Pure Math.. Amer. Math. Soc., Providence, R.I., pp. 5665
 Rabin, M. O. (1960) Computable algebra, general theory and theory of computable fields. Trans. Amer. Math. Soc. 95: pp. 341360 CrossRef
 Waerden, B. L. (1949) Modern Algebra. Ungar, New York
 Title
 Sets of degrees of computable fields
 Journal

Israel Journal of Mathematics
Volume 27, Issue 34 , pp 348356
 Cover Date
 19770901
 DOI
 10.1007/BF02756493
 Print ISSN
 00212172
 Online ISSN
 15658511
 Publisher
 SpringerVerlag
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 Authors

 Elie Bienenstock ^{(1)}
 Author Affiliations

 1. The Hebrew University of Jerusalem, Jerusalem, Israel