On the extensions of Di Nola's Theorem

TL;DR

This paper provides a direct proof of Di Nola's representation theorem for MV-algebras and extends it to rational-restricted standard MV-algebras, enhancing understanding of their structure and embeddings.

Contribution

It offers a new direct proof of Di Nola's theorem and extends the results to rational-restricted MV-algebras, broadening the theorem's applicability.

Findings

Finite partial subalgebras embed into rational interval [0,1]

Direct proof simplifies understanding of MV-algebra representations

Extension to rational-restricted MV-algebras established

Abstract

The main aim of this paper is to present a direct proof of Di Nola's representation Theorem for MV-algebras and to extend his results to the restriction of the standard MV-algebra on rational numbers. The results are based on a direct proof of the theorem which says that any finite partial subalgebra of a linearly ordered MV-algebra can be embedded into $\mathbb Q\cap [0,1].$