Background
Zaring, Wilson Miles was born on November 9, 1926 in Finchville, Kentucky, United States. Son of Wilson Coots and Susan Fontain (Miles) Zaring.
(In 1963, the first author introduced a course in set theo...)
In 1963, the first author introduced a course in set theory at the Uni versity of Illinois whose main objectives were to cover G6del's work on the consistency of the axiom of choice (AC) and the generalized con tinuum hypothesis (GCH), and Cohen's work on the independence of AC and the GCH. Notes taken in 1963 by the second author were the taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in set theory frequently develop the subject rapidly moving from key result to key result and suppressing many details. Advocates of the fast development claim at least two advantages. First, key results are highlighted, and second, the student who wishes to master the sub ject is compelled to develop the details on his own. However, an in structor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text. We have chosen instead a development that is quite detailed and complete. For our slow development we claim the following advantages. The text is one from which a student can learn with little supervision and instruction. This enables the instructor to use class time for the presentation of alternative developments and supplementary material.
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(This text deals with three basic techniques for construct...)
This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain funda mental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "I ntroduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have inc1uded in the introductory material al1 the results from Boolean algebra and topology that we need. When notation from our first volume is introduced, it is accompanied with a deflnition, usually in a footnote. Consequently a reader who is familiar with elementary set theory will find this text quite self-contained.
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educator mathematician university administrator
Zaring, Wilson Miles was born on November 9, 1926 in Finchville, Kentucky, United States. Son of Wilson Coots and Susan Fontain (Miles) Zaring.
AB, Kentucky Wesleyan College, Owensboro, 1950. Master of Science, University Kentucky, Lexington, 1952. Doctor of Philosophy, University Kentucky, Lexington, 1955.
Instructor, University of Illinois, Urbana, 1955-1957; assistant professor, University of Illinois, Urbana, 1957-1963; associate professor, University of Illinois, Urbana, 1963-1991; associate professor emeritus, since 1991; associate director Academy Year Institute, University of Illinois, Urbana, 1958-1964; director Academy Year Institute, University of Illinois, Urbana, 1964-1973; assistant to head mathematics, University of Illinois, Urbana, 1973-1978; graduate advisor mathematics, University of Illinois, Urbana, 1978-1982; director graduate studies mathematics, University of Illinois, Urbana, 1982-1991. Consultant Comprehensive School Mathematics Project, Carbondale, Illinois, 1974-1984.
(In 1963, the first author introduced a course in set theo...)
(In 1963, the first author introduced a course in set theo...)
(This text deals with three basic techniques for construct...)
Corporal United States Marine Corps Reserve, 1945-1947.
Married Marjorie Jane Calvert, August 25, 1950. Children: David Wilson, Susan Claire.