This is the proceedings of the AMS special session on nonstandard models of arithmetic and set theory held at the Joint Mathematics Meetings in Baltimore (MD).

This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Written in an inf

Non-standard models of arithmetic are of interest to mathematicians through the presence of infinite integers and the various properties they inherit from the f

This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive form

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argu