Wolf R. A Tour Through Mathematical Logic 2005

Textbook in PDF and DJVU formats

The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Gödel's incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about the subject.
Predicate Logic
Axiomatic Set Theory
Recursion Theory and Computability
Gödel's Incompleteness Theorems
Model Theory
Contemporary Set Theory
Nonstandard Analysis
Constructive Mathematics
A Deductive System for First-order Logic
B Relations and Orderings
C Cardinal Arithmetic
D Groups, Rings, and Fields