A Concise Introduction to Mathematical Logic
by Wolfgang Rautenberg
Publisher: Springer 2009
Number of pages: 131
The textbook by Professor Wolfgang Rautenberg is a well-written introduction to the beautiful and coherent subject of mathematical logic. It contains classical material such as logical calculi, beginnings of model theory, and Goedel's incompleteness theorems, as well as some topics motivated by applications, such as a chapter on logic programming.
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by Wolfram Pohlers, Thomas Glass
This text treats pure logic and in this connection introduces to basic proof-theoretic techniques. Fundamentals of model theory and those of recursion theory are dealt with. Furthermore, some extensions of first order logic are treated.
by P.D. Magnus
An introduction to sentential logic and first-order predicate logic with identity, logical systems that influenced twentieth-century analytic philosophy. The book should help students understand quantified expressions in their philosophical reading.
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 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.