The Art of Logic
by Nuel Belnap
Publisher: University of Pittsburgh 2009
Number of pages: 314
Contents: Grammar; The art of the logic of truth-functional connectives; Quantifier proofs; A modicum of set theory; Symbolizing English quantifiers; Quantifier semantics - interpretation and counterexample; Theories; Definitions.
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by Stefan Bilaniuk
An introduction to mathematical logic for undergraduates. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is to learn the material by solving the problems.
by Christopher C. Leary, Lars Kristiansen - Milne Library Publishing
In this book, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study.
by Christopher Gauker - University of Cincinnati
This book is for anyone who has had a solid introductory logic course and wants more. Topics covered include soundness and completeness for first-order logic, Tarski's theorem on the undefinability of truth, Godel's incompleteness theorems, etc.
by H. Andreka, I. Nemeti, I. Sain
Part I of the book studies algebras which are relevant to logic. Part II deals with the methodology of solving logic problems by (i) translating them to algebra, (ii) solving the algebraic problem, and (iii) translating the result back to logic.