# An exposition of the compactness of $L(Q^\mathrm{cf})$

## TL;DR

This paper provides an exposition on the compactness properties of the logic $L(Q^{cf})$, which involves the class of regular cardinals, highlighting its foundational aspects.

## Contribution

It offers a detailed explanation of the compactness theorem for $L(Q^{cf})$ logic across any set of regular cardinals, clarifying its theoretical framework.

## Key findings

- Establishes the compactness of $L(Q^{cf})$ for all sets of regular cardinals.
- Clarifies the foundational aspects of $L(Q^{cf})$ logic.
- Provides a comprehensive exposition of the logic's properties.

## Abstract

We give an exposition of the compactness of $L(Q^\mathrm{cf})$, for any set $C$ of regular cardinals.