The preface says: "Computability and Logic is intended for the student in philosophy or pure or applied mathematics who has mastered the material ordinarily covered in a first course in logic and who wishes to advance his or her acquaintance with the subject. The aim of the book is to present the principal fundamental theoretical results about logic, and to cover certain other meta-logical results whose proofs are not easily obtainable elsewhere."
I find the style to be more chatty and less dry than most mathematical texts, presumably to cater for the philosophy students. The main prerequisite is an understanding of first-order logic. The Wikipedia page for "First-order logic" looks pretty good.
I really like Boolos and Jeffrey's "Computability and Logic", although that would probably count as a second course. What level of background knowledge do you already have?
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The preface says: "Computability and Logic is intended for the student in philosophy or pure or applied mathematics who has mastered the material ordinarily covered in a first course in logic and who wishes to advance his or her acquaintance with the subject. The aim of the book is to present the principal fundamental theoretical results about logic, and to cover certain other meta-logical results whose proofs are not easily obtainable elsewhere."
I find the style to be more chatty and less dry than most mathematical texts, presumably to cater for the philosophy students. The main prerequisite is an understanding of first-order logic. The Wikipedia page for "First-order logic" looks pretty good.
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