Abstract
0. Introduction 203 A. History and explanation of the problem 203 B. Background from logic and elimination theory 208 1. Generalizing the quantifier elimination problem . 210 A. Notations and terminology 210 B. The Frobenius symbol 212 C. Galois stratification and generalization of the diophantine problem .213 2. The intersection-union process 215 A. The intersection-union process over a finite field 215 B. The intersection-union process over a perfect field 217 3. A generalization of the theorems of Bertini and Noether . 219 4. Diophantine problems over all residue class fields of a number field . . .225 5. Diophantine problems over finite fields . 230 A. Over all extensions of a fixed finite field 230 B. Over all finite fields 231
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