A second course in logic
| Abstract | This is a free book, 165 pages. It 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, Gödel's incompleteness theorems, the undecidability of first-order logic, a smattering of second-order logic, and modal logic (both propositional and quantificational). I wrote it for use in my own course, because I thought I could present the most important results and concepts more clearly than the available textbooks. | |||||||||
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Giangiacomo Gerla & Virginia Vaccaro (1984). Modal Logic and Model Theory. Studia Logica 43 (3):203 - 216.
Vilém Novák (1987). First-Order Fuzzy Logic. Studia Logica 46 (1):87 - 109.
Alexander Paseau (2010). Pure Second-Order Logic with Second-Order Identity. Notre Dame Journal of Formal Logic 51 (3):351-360.
Balder ten Cate (2006). Expressivity of Second Order Propositional Modal Logic. Journal of Philosophical Logic 35 (2).
Balder ten Cate (2006). Expressivity of Second Order Propositional Modal Logic. Journal of Philosophical Logic 35 (2):209 - 223.
Theodore Sider (2010). Logic for Philosophy. Oxford University Press.
P. B. Andrews (2002). An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Kluwer Academic Publishers.
Richard Kaye (2007). The Mathematics of Logic: A Guide to Completeness Theorems and Their Applications. Cambridge University Press.
G. Aldo Antonelli & Richmond H. Thomason (2002). Representability in Second-Order Propositional Poly-Modal Logic. Journal of Symbolic Logic 67 (3):1039-1054.
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