Pacific Journal of Mathematics

Pseudofinite fields, procyclic fields and model-completion.

Allan Adler and Catarina Kiefe

Article information

Source
Pacific J. Math., Volume 62, Number 2 (1976), 305-309.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102867717

Mathematical Reviews number (MathSciNet)
MR0419213

Zentralblatt MATH identifier
0339.02048

Subjects
Primary: 02H15
Secondary: 12L10: Ultraproducts [See also 03C20]

Citation

Adler, Allan; Kiefe, Catarina. Pseudofinite fields, procyclic fields and model-completion. Pacific J. Math. 62 (1976), no. 2, 305--309. https://projecteuclid.org/euclid.pjm/1102867717


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References

  • [1] James Ax, Solving diophantine problems modulo every prime, Ann. of Math.,85 (1967), 161-183.
  • [2] James Ax, The elementary theory of finite fields, Ann. of Math., 88 (1968), 239-271.
  • [3] S. Shelah, Every two elementarily equivalent models have isomorphic ultrapowers,Israel J. Math.
  • [4] Moshe Jarden, Elementary statements over large algebraic fields, doctoral thesis, The Hebrew University of Jerusalem (1969).
  • [5] Catarina Kiefe, On the rationality of a zeta-function of a set definable over a finite field, doctoral thesis, S.U.N.Y. Stony Brook (1973).
  • [6] Serge Lang, Diophantine geometry, Interscience Tracts No. 11 (1962).
  • [7] G. Sacks, Saturated model theory, Benjamin (1972).
  • [8] A. Robinson, Nonstandard Arithmetic, Bull. Amer. Math. Soc, 73 (1967), 818-843.