Bounded pregeometries and pairs of fields
Leonardo Angel (1), Lou van den Dries (2) ((1) Universidad de los, Andes, Bogota-Colombia, (2) University of Illinois at Urbana-Champaign,, Illinois)
TL;DR
This paper introduces a bounded pregeometry concept for pairs of algebraically closed and real closed fields, establishing conditions for definable sets to be co-analyzable relative to the subfield.
Contribution
It provides a new framework for understanding definable sets in pairs of fields through bounded pregeometries, extending results to tame pairs of real closed fields.
Findings
Definable sets in pairs are co-analyzable iff almost internal to the subfield
Introduction of a bounded pregeometry for pairs of fields
Extension of results to tame pairs of real closed fields
Abstract
A definable set in a pair (K, k) of algebraically closed fields is co-analyzable relative to the subfield k of the pair if and only if it is almost internal to k. To prove this and some related results for tame pairs of real closed fields we introduce a certain kind of bounded pregeometry for such pairs.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology