Punctually presented structures I: Closure theorems

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.

Effective Presentations of Mathematical Structures

“…The general case was left open. The main goal is to give a systematic primitive recursive analysis of primitive recursive closure theorems in algebra [DM23]. The next result of the thesis is the following theorem which, in particular, answers the aforementioned question raised in [SS21] by Selivanov and Selivanova.…”