Abstract
We prove that each perfect Frobenius field is algebraically bounded and hence has a dimension function in the sense of v.d. Dries on the collection of all definable sets. Given a definable set S over Q (resp. Fp) we can effectively determine for each k ∊ {—∞,0,1,…} whether there exists a perfect Frobenius field M of characteristic 0 (resp., of characteristic p) such that the dimension of S(M) is k. Our method of proof and decision procedure is based on Galois Stratification.
Original language | English |
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Pages (from-to) | 43-64 |
Number of pages | 22 |
Journal | Forum Mathematicum |
Volume | 6 |
Issue number | 6 |
DOIs | |
State | Published - 1994 |