"The aim of this book is to present the strongest possible version of
G¨odel's incompleteness theorem, using an information-theoretic approach
based on the size of com...
The Interpolation Theorem, first formulated and proved by W. Craig fifty years ago for predicate logic, has been extended to many other logical frameworks and is being applied in s...
We propose here an extension of Rice's Theorem to first-order logic, proven by totally elementary means. If P is any property defined over the collection of all first-order t...
Abstract. We use the theorem prover Isabelle to formalise and machinecheck results of the theory of generalised substitutions given by Dunne and used in the B method. We describe t...
Abstract. We discuss what constitutes knowledge in pure mathematics and how new advances are made and communicated. We describe the impact of computer algebra systems, automated th...