With the work of Hilbert and the publication of the Principia mathematica by Russell and Whitehead early in this century and Godel's work in the 1930's on incompleteness in mathematics, the issues of provability and incompleteness theorems have been of central concern for logicians, mathematicians and philosophers of mathematics. In 1976, Professor Boolos completed a major study which resulted in his book, The Unprovability of Consistency . Since that time, much has happened in the logic of provability which requires a new look at the issues addressed in that original study. Provability logic, a branch of modal logic, is the study of those properties of formal consistency and provability (as in the work of Hilbert and Godel) that can be expressed when a symbol meaning "it is provable that" is added to the usual languages of logic. As Godel discovered in his studies of mathematics, formal provability is a perplexing notion: although every interesting formal theory T can prove "2+2=4" provable.in.T, no such theory T can prove even "2+2=5" un provable.in.T. Provability logic provides a systematic account of formal provability that makes sense of its strange properties. The field has grown greatly since 1976. One striking new feature of his new study will be the treatment of predicate (i.e., quantified) provability logic, including recent results by Artyomov, McGee, Vandanyan and Professor Boolos himself. This and other new topics will greatly enhance our understanding of the logic of provability and incompleteness theorems.
