Work

Results in model theory for Riesz-valued structures

Year: 2025

Type: article

Abstract: We study model-theoretic properties of a logic whose formulas take values in suitable Riesz spaces. In addition to having a set of truth values which is not linearly ordered, there is no absolute truth or falsehood value. We take inspiration from the version of continuous logic developed in [8] by Ben-Yaacov et al. and from the more general approach recently proposed in [11] by Keisler. We extend to our framework a number of results obtained by the above mentioned authors. Under suitable assumptions on the underlying Riesz space, we provide an ultraproduct construction and prove a Łoś theorem, from which compactness follows. In the framework of Riesz spaces we also address definability issues and we extend metric notions, obtaining analogues of Keisler’s pre-metric structures and pre-metric expansions of theories defined in Keisler. In particular, we prove that every theory in a countable language has a pre-metric expansion with a so-called pseudometric approximate distance.

Source: Archive for Mathematical Logic

DOI: 10.1007/s00153-025-00990-5

Author: Stefano Baratella

Institution: University of Trento

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Università degli Studi di Trento