Reverse Mathematics

Damir D. Dzhafarov is an Associate Professor of Mathematics at the University of Connecticut. He obtained his PhD from the University of Chicago, and has held postdoctoral positions at the University of Notre Dame and the University of California, Berkeley. He has held visiting positions at the National University of Singapore and Charles University, Prague. His research focuses on the computability theoretic and reverse mathematical aspects of of combinatorics, and on the interactions of reverse mathematics with computable analysis and other areas.Carl Mummert is a Professor of Computer and Information Technology at Marshall Univeristy. He obtained his Ph.D. from Pennsylvania State University and held postdoctoral positions at Appalachian State University and the University of Michigan.  His research has included the reverse mathematics of topology and combinatorics as well as higher order reverse mathematics.

“This book takes a broad approach to reverse mathematics, emphasizing connections to computability theory and Weihrauch analysis. It will serve well as a text for courses in reverse mathematics and as a reference for researchers in the area.” (Jeffry L. Hirst, zbMATH 1555.03002, 2025) “Dzhafarov and Mummert's book provides a systematic introduction to new developments in reverse mathematics based on a computability-theoretic approach … . This book is a valuable reference for students and researchers working on reverse mathematics as well as otherbranches of mathematical logic.” (Huishan Wu, Mathematical Reviews, September, 2023)

• 1 introduction.- Part I Computable mathematics: 2 Computability theory.- 3 Instance–solution problems.- 4 Problem reducibilities.- Part II Formalization and syntax: 5 Second order arithmetic.- 6 Induction and bounding.- 7 Forcing.- Part III Combinatorics: 8 Ramsey’s theorem.- 9 Other combinatorial principles.- Part IV Other areas: 10 Analysis and topology.- 11 Algebra.- 12 Set theory and beyond.