## Achievements

Posted: Wednesday, May 15, 2024### Daniel Cunningham, Professor Emeritus, Mathematics

Daniel Cunningham, professor emeritus of mathematics, has signed a contract with Cambridge University Press to complete and publish a second edition of his mathematics book *Set Theory: A First Course*. In the first edition, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, the ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The five anonymous reviewers who assessed Cunningham's proposal for a second edition offered many helpful comments and recommendations. As a result, the second edition will now contain the following new topics: set theoretic constructions of the integers, the rational numbers, the real numbers, and the hyperreals. We will also prove theorems that demonstrate that the standard definitions of limit, continuity, and the derivative have equivalent versions in the hyperreals using infinitesimals. A new final chapter will cover models of set theory and will end with a discussion on Kurt Gödel’s inner model of constructible sets and on Paul Cohen's method of forcing. The second edition will also contain solutions to all the exercises.

Cambridge University Press (CUP) is the publishing house of the University of Cambridge. Dedicated to excellence, its purpose is to further the university's objective of advancing knowledge, education, learning, and research worldwide. Cambridge is a leading global publisher in pure and applied mathematics, with an extensive program of high-quality books and journals that reaches into every corner of the subject. CUP's catalog reflects not only the breadth of mathematics but also its depth, with titles for undergraduate students, for graduate students, for researchers, and for users of mathematics. Cambridge University Press has over 50 offices around the globe, and it distributes its products to nearly every country in the world.