Many Valued Algebras

This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic.

This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work.

This monograph provides a modern introduction to the theory of quantales.
First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to theoretical computer science. This book recasts the subject within the powerful framework of categorical algebra, showcasing its versatility through applications to C*- and MV-algebras, fuzzy sets and automata. With exercises and historical remarks at the end of each chapter, this self-contained book provides readers with a valuable source of references and hints for future research.

This volume has been curated from two sources: presentations from the Conference on Rings and Polynomials, Technische Universität Graz, Graz, Austria, July 19 –24, 2021, and papers intended for presentation at the Fourth International Meeting on Integer-valued Polynomials and Related Topics, CIRM, Luminy, France, which was cancelled due to the pandemic. The collection ranges widely over the algebraic, number theoretic and topological aspects of rings, algebras and polynomials. Two areas of particular note are topological methods in ring theory, and integer valued polynomials. The book is dedicated to the memory of Paul-Jean Cahen, a coauthor or research collaborator with some of the conference participants and a friend to many of the others. This collection contains a memorial article about Paul-Jean Cahen, written by his longtime research collaborator and coauthor Jean-Luc Chabert.