Introduction to Mathematical Logic: A problem solving course
by Arnold W. Miller
Publisher: arXiv 1996
Number of pages: 75
This is a set of 288 questions written for a Moore-style 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; Lowenheim-Skolem theorems; Turing machines, Church's Thesis; completeness theorem and first incompleteness theorem; undecidable theories; second incompleteness theorem.
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by Nuel Belnap - University of Pittsburgh
This course assumes you know how to use truth functions and quantifiers as tools. Our task here is to study these very tools. Contents: logic of truth functional connectives; first order logic of extensional predicates, operators, and quantifiers.
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.
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.
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.