Handbook of Mathematical Logic with Applications

This handbook surveys introductory mathematical logic and provides examples of applications in set theory, combinatorics, and algebra.  Professionals and students alike will benefit from the book's comprehensive collection of topics within mathematical logic, including propositional logic, predicate logic, proof theory, naive set theory, axiomatic set theory, combinatorics, axiomatic number theory, ordinals, cardinals, model theory, consistency, incompleteness, groups, abelian groups, modules, and compactness.  References to important techniques within these areas are presented in an effort to illustrate the main concepts and techniques.  An introductory review of mathematical proof-writing is provided with examples from number theory, relations, function, groups, and topology.  Each topic is accompanied by an introduction, historical notes, real-world examples and applications as well as references for further study.  Partial solutions to the presented proofs are also provided to further aid in reader comprehension.  While the necessary fundamental coverage is provided, more advanced topics are also provided for those interested in gaining a deeper understanding of the field.