Henkin constructions of models with size continuum

TL;DR

This paper reviews the Henkin construction method for creating models of size continuum, providing new proofs of existing results and introducing a new theorem linking pseudominimal theories to atomic models of continuum size.

Contribution

It offers a comprehensive survey of Henkin constructions and presents a novel theorem connecting pseudominimal theories with atomic models of size continuum.

Findings

New proof techniques for models of size continuum

A joint theorem showing pseudominimal theories have atomic models of continuum size

Enhanced understanding of model construction methods

Abstract

We survey the technique of constructing customized models of size continuum in omega steps and illustrate the method by giving new proofs of mostly old results within this rubric. One new theorem, which is joint with Saharon Shelah, is that a pseudominimal theory has an atomic model of size continuum.