This is the metatheory for SL and PL from Paul Teller's book. (Thanks Paul!) I've just linked to some of the last chapters of the book. The rest of the book can be found at:

A Modern Formal Logic Primer

by Paul Teller


Chapter 10, Metatheory: The Basic Concepts

Chapter 11, Mathematical Induction

Chapter 13, Soundness and Completeness for Sentence Logic Derivations

Chapter 14, Koenig's Lemma, Compactness, and Generalization to Infinite Sets of Premises

Chapter 15, Interpretations, Soundness, and Completeness for Predicate Logic