Volume I provides a detailed analysis of cylindric algebras, starting with a formulation of their axioms and a development of their elementary properties, and proceeding to a deeper study of their interrelationships by means of general algebraic notions such as subalgebras, homomorphisms, direct products, free algebras, reducts and relativized algebras.

§1. Introduction. This paper deals with aspects of my doctoral dissertation which contributed to the early development of model theory. What was of use to later workers was less the results of my thesis, than the method by which I proved the completeness of first-order logic—a result established by Kurt Gödel in his doctoral thesis 18 years before.The ideas that fed my discovery of this proof were mostly those I found in the teachings and writings of Alonzo Church. This may (...) seem curious, as his work in logic, and his teaching, gave great emphasis to the constructive character of mathematical logic, while the model theory to which I contributed is filled with theorems about very large classes of mathematical structures, whose proofs often by-pass constructive methods.Another curious thing about my discovery of a new proof of Gödel's completeness theorem, is that it arrived in the midst of my efforts to prove an entirely different result. Such “accidental” discoveries arise in many parts of scientific work. Perhaps there are regularities in the conditions under which such “accidents” occur which would interest some historians, so I shall try to describe in some detail the accident which befell me.A mathematical discovery is an idea, or a complex of ideas, which have been found and set forth under certain circumstances. The process of discovery consists in selecting certain input ideas and somehow combining and transforming them to produce the new output ideas. The process that produces a particular discovery may thus be represented by a diagram such as one sees in many parts of science; a “black box” with lines coming in from the left to represent the input ideas, and lines going out to the right representing the output. To describe that discovery one must explain what occurs inside the box, i.e., how the outputs were obtained from the inputs. (shrink)

About a month after his 83rd birthday Raphael Robinson was almost wholly incapacitated by a massive stroke, and 8 weeks later, on January 27, 1995, he died of ensuing complications. Mathematics was his life. He was always working on problems—those brought to him in journals or by colleagues, and others that he invented. Just three days before his death he received word that a paper of his, originating in a published problem, was accepted for publication. His 64 publications spanned a (...) full 6 decades, and included significant papers on number theory, combinatorics, complex analysis, and geometry, in addition to logic and set theory.Robinson was born on November 2, 1911, in National City, California. He came to Berkeley to study mathematics, obtaining an A.B. in 1932, an M.A. in 1933, and his Ph.D. in December, 1934. His dissertation was in complex analysis. He took 12 graduate courses in a variety of fields, but not one was close to logic or set theory—which was later the setting of about a quarter of his publications.After completing his studies Robinson served as Instructor for two years at Brown University, then returned for good to Berkeley in 1937, reaching the rank of full Professor in 1949. He taught a great variety of courses and was known as an excellent teacher, but was most interested in problemsolving and research and in 1972, at age 61, he elected early retirement, at considerable financial sacrifice, in order to concentrate on these pursuits. (shrink)