Abstract

Andrzej Mostowski, whose previous book on Gödel's incompleteness theorem is widely acclaimed as a modern classic on the subject, now gives us a series of sixteen beautifully clear lectures on the development of logic and foundations of mathematics during the past thirty years. A very wide range of subjects is treated in this book, from the intuitionistic logic and the Gödel work on the incompleteness of arithmetic to the set-theoretical results of Cohen and the algebraic theory of direct and reduced products. The notable thing about all this is that the book is everywhere readable by the non-expert. Anyone who has had an elementary course in mathematical logic and set theory can read this book with a great deal of profit. Moreover, the exposition sparkles with Mostowski's remarks, conjectures and speculations on the philosophy of mathematics and the future of foundational studies. There are very few rigorously proved theorems in the book—as this was not its purpose—but a bibliography of 244 pertinent items is furnished at the end of the book for those who would like to pursue the material to greater depth.—H. P. K.