Nominal sets. Names and symmetry in computer science (Q2849600)

This book deals with the use of atomic (non-structured) names in computer science from a rigorous and systematic perspective. To this end, the theory of \(G\)-sets is developed in all its details, allowing to introduce the Boolean topos \(\mathrm{Nom}\) of nominal sets, where concepts such as freshness of a name, name abstraction and orbit-finiteness can find a natural and rigorous setting. A precise comparison is also made with other partial attempts in the same direction, that occurred during the years to make rigorous the concepts mentioned above when used in sophisticated situations, both in mathematics and in computer science. Here, the author is not afraid to use all the means provided by category/topos theory, aiming to set at the right degree of abstraction the concepts he is interested in. In this way several important topics, particularly in logic and in denotational semantics, are rethought and placed into a new perspective.