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This is a comprehensive book on the life and works of Leon Henkin
(1921-2006), an extraordinary scientist and excellent teacher whose
writings became influential right from the beginning of his career
with his doctoral thesis on "The completeness of formal systems"
under the direction of Alonzo Church. Upon the invitation of Alfred
Tarski, Henkin joined the Group in Logic and the Methodology of
Science in the Department of Mathematics at the University of
California Berkeley in 1953. He stayed with the group until his
retirement in 1991. This edited volume includes both foundational
material and a logic perspective. Algebraic logic, model theory,
type theory, completeness theorems, philosophical and foundational
studies are among the topics covered, as well as mathematical
education. The work discusses Henkin's intellectual development,
his relation to his predecessors and contemporaries and his impact
on the recent development of mathematical logic. It offers a
valuable reference work for researchers and students in the fields
of philosophy, mathematics and computer science.
This book gives a comprehensive introduction to Universal Algebraic
Logic. The three main themes are (i) universal logic and the
question of what logic is, (ii) duality theories between the world
of logics and the world of algebra, and (iii) Tarskian algebraic
logic proper including algebras of relations of various ranks,
cylindric algebras, relation algebras, polyadic algebras and other
kinds of algebras of logic. One of the strengths of our approach is
that it is directly applicable to a wide range of logics including
not only propositional logics but also e.g. classical first order
logic and other quantifier logics. Following the Tarskian
tradition, besides the connections between logic and algebra,
related logical connections with geometry and eventually spacetime
geometry leading up to relativity are also part of the perspective
of the book. Besides Tarskian algebraizations of logics, category
theoretical perspectives are also touched upon. This book, apart
from being a monograph containing state of the art results in
algebraic logic, can be used as the basis for a number of different
courses intended for both novices and more experienced students of
logic, mathematics, or philosophy. For instance, the first two
chapters can be used in their own right as a crash course in
Universal Algebra.
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