The logic of provability.

*(English)*Zbl 0891.03004
Cambridge: Cambridge University Press. xxxvi, 276 p. (1993).

Publisher’s description: This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author’s earlier The Unprovability of Consistency (1979; Zbl 0409.03009). Modal logic is concerned with the notions of necessity and possibility. What George Boolos does is to show how the concepts, techniques and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Gödel and the self-referential sentences constructed in their proof. The book explores the effects of reinterpreting the notions of necessity and possibility to mean provability and consistency. It contains the first application of quantified modal logic to formal provability.

##### MSC:

03B45 | Modal logic (including the logic of norms) |

03F40 | Gödel numberings and issues of incompleteness |

03F30 | First-order arithmetic and fragments |

03-02 | Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations |