Differential Specializations in Integral and Algebraic Extensions

Abstract

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New examples (and counterexamples) of complete finite-rank differential varieties

“…The research thread we add to in this paper has two main strands. The first is differential algebraic and is comprised mainly of the papers [6] of Kolchin, [1], [2] of P. Blum, and [9], [10] of Morrison. The second strand incorporates model-theoretic ingredients.…”

“…Three additional results due to Morrison are critical to our work on δ-completeness; they are Proposition 4 and its corollary in [9] and Corollary 3.2 in [10].…”

Complete Sets in Differentially Closed Fields

“…The result of van den Dries in the previous section ties this problem with the problem of extending δ-homomorphisms. The latter subject was studied by Blum [3] and Morrison [11,12]. Here we gather a few basic facts and introduce some terminology that we are going to use.…”

“…I also thank Phyllis Cassidy who introduced me to [8,11,12] and showed me Ritt's example of the "anomaly of differential dimension of intersections" which is closely related to Kolchin's example in Section 2.…”

Closedness of morphisms of differential algebraic sets. Applications to system theory

“…, τ μ are the coordinate functions on it. 6 Since the completion of this paper we have come accross the work [12], thanks to one of the anonymous reviewers. The proof (but not the Statement) of Theorem 2 may be derived from that paper.…”