Symbolic Logic: A First Course
by Gary Hardegree
Publisher: Mcgraw-Hill College 1999
Number of pages: 468
Contents: Basic Concepts of Logic; Truth-Functional Connectives; Validity in Sentential Logic; Translations in Sentential Logic; Derivations in Sentential Logic; Translations in Monadic Predicate Logic; Translations in Polyadic Predicate Logic; Derivations in Predicate Logic.
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by Nuel Belnap - University of Pittsburgh
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.
by Arnold W. Miller - arXiv
This is a set of questions written for a course in Mathematical Logic. Topics covered are: propositional logic; axioms of ZFC; wellorderings and equivalents of AC; ordinal and cardinal arithmetic; first order logic, and the compactness theorem; etc.
by Bertrand Russell - University of Massachusetts Amherst
A very accessible mathematical classic. It sets forth in elementary form the logical definition of number, the analysis of the notion of order, the modern doctrine of the infinite, and the theory of descriptions and classes as symbolic fictions.
by Edward Nelson - Princeton Univ Pr
The book based on lecture notes of a course given at Princeton University in 1980. From the contents: the impredicativity of induction, the axioms of arithmetic, order, induction by relativization, the bounded least number principle, and more.