Model theory of second order logic

TL;DR

This paper surveys the model theory of second order logic, exploring its properties, limitations, and the differences from first order logic in a comprehensive manner.

Contribution

It provides an overview of the key results and open problems in the model theory of second order logic, highlighting its unique features.

Findings

Second order logic has richer expressive power than first order logic.

Model theory of second order logic faces limitations such as lack of completeness.

The survey identifies key open problems and research directions.

Abstract

This is a survey of the model theory of second order logic.