On models of affine arithmetic

2025/08/25 by Bagheri, Seyed-Mohammad
#03C62 #03C66 #03H15 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2508.18266

Abstract

By affine arithmetic is meant the set of affine consequences of Peano arithmetic. This is a continuous theory which is studied in the framework of affine logic, a sublogic of continuous logic. Affine arithmetic is undecidable. Also, its models are generally lattice ordered and carry a nontrivial metric. Classical models are then characterized as those which are linearly ordered. In this paper, the affine variants of several classical results in Peano arithmetic are proved. In particular, an affine form of Gaifman's splitting theorem is proved.

Citations

• Extremal models and direct integrals in affine logic
• Extreme types and extremal models
• The isomorphism theorem for linear fragments of continuous logic

Related

• Elements of affine model theory
• Stability in affine logic
• Extremal models and direct integrals in affine logic
• Definability in affine continuous logic
• AFFINE LOGIC FOR CONSTRUCTIVE MATHEMATICS