Model theoretic forcing in analysis

TL;DR

This paper introduces a new framework for model theoretic forcing applicable beyond first-order logic, with specific applications demonstrated in Banach space theory.

Contribution

It develops a novel non-first-order model theoretic forcing framework and applies it to problems in Banach space theory.

Findings

Established a new forcing framework for non-first-order contexts

Applied the framework to solve problems in Banach space theory

Provided insights into the structure of Banach spaces using model theory

Abstract

We present a framework for model theoretic forcing in a non-first-order context, and present some applications of this framework to Banach space theory.