Yasumoto , Nonstandard arithmetic of function fields 11

References

[ 1 ] E. Kani, Nonstandard diophantische Geometrie, insbesondere Satz von Mordeil-Weil, Inaugural- tation, Heidelberg 1978.

[ 2 ] A, Robinson, Nonstandard arithmetic, Bull. Amer. Math. Soc. 73 (1967), 818 - 843.

13'i A. Robinson, Algebraic function fields and nonstandard arithmetic, in: Contribution to nonstandard analysis, W. A. J. Luxemberg and A. Robinson, Eds., Amsterdam 1972.

[ 4 ] A. Robinson, Nonstandard points on algebraic curves, J. Number Theory 5 (1973), 301 327.

[ 5 ] A. Robinson and P. Roquette, On the finiteness theorem of Siegel and Mahler concerning diophantine equations, J. Number Theory 7 (1975), 121 -176.

[ 6 ] P. Roquette, Nonstandard aspects of Hilbert's irreducible theorem. Lecture Notes in Math. 498, 231 274.

[ 7 ] C. Runge, Über ganzzahlige Lösungen von Gleichungen zwischen zwei Veränderlichen, J. reine angew. Math. 100(1887), 425-435.

[ 8 ] T. Skolem, Diophantische Gleichungen, Ergebn. d. Math. 4 (1938).

[ 9 ] A. Weil, Arithmetic on algebraic varieties, Ann. Math. 53 (1951), 412 444.

Department of Mathematics, Faculty of Science, Nagoya University, Chikusa-ku Nagoya, 464, Japan

Eingegangen 25. Mai 1982