Punctually presented structures I: Closure theorems

Issue title: Special issue on the occasion of Victor Selivanov’s 70th birthday

Guest editors: Nikolay Bazhenov, Takayuki Kihara and Svetlana Selivanova

Article type: Research Article

Authors: Dorzhieva, Marina^{a; *} | Melnikov, Alexander^b

Affiliations: [a] School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand | [b] School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand

Correspondence: [*] Corresponding author. dm-3004@inbox.ru.

Abstract: We study the primitive recursive content of various closure results in algebra and model theory, including the algebraic, the real, and the differential closure theorems. In the case of ordered fields and their real closures, our result settles a question recently raised by Selivanova and Selivanov.

Keywords: Primitive recursion, algebraic closure, constructive models

DOI: 10.3233/COM-230448

Journal: Computability, vol. 12, no. 4, pp. 323-337, 2023