A.P. Morse’s Set Theory and Analysis

Buch | Softcover

LXXXI, 454 Seiten

2023
Springer International Publishing (Verlag)
978-3-031-05357-3 (ISBN)

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This volume explores A.P. Morse's (1911-1984) development of a formal language for writing mathematics, his application of that language in set theory and mathematical analysis, and his unique perspective on mathematics. The editor brings together a variety of Morse's works in this compilation, including Morse's book A Theory of Sets, Second Edition (1986), in addition to material from another of Morse's publications, Web Derivatives, and notes for a course on analysis from the early 1950's. Because Morse provided very little in the way of explanation in his written works, the editor's commentary serves to outline Morse's goals, give informal explanations of Morse's formal language, and compare Morse's often unique approaches to more traditional approaches. Minor corrections to Morse's previously published works have also been incorporated into the text, including some updated axioms, theorems, and definitions. The editor's introduction thoroughly details the corrections and changes made and provides readers with valuable insight on Morse's methods.
A.P. Morse's Set Theory and Analysis will appeal to graduate students and researchers interested in set theory and analysis who also have an interest in logic. Readers with a particular interest in Morse's unique perspective and in the history of mathematics will also find this book to be of interest.

Robert A. Alps is a retired pension actuary living in Evanston, Illinois. His Ph. D. dissertation at Northwestern University dealt with Morse's formal language. He assisted Morse in the preparation of the second edition of A Theory of Sets (1986).

Preface.- Editor's Introduction.- Language and Inference.- Logic.- Set Theory.- Elementary Analysis.- Metrics.- Measure.- Linear Measure and Total Variation.- Integration.- Product Measures.- Web Derivatives.- Classical Differentiation.- The Construction of Definition.- The Consistency of the Axiom of Size.- Suggested Reading.- Publications of A.P. Morse.- Errata to A Theory of Sets, Second Edition.- Integration with Respect to Addor Functions.- The Henstock-Kurzweil Integral.

Erscheinungsdatum	27.08.2023
Zusatzinfo	LXXXI, 454 p.
Verlagsort	Cham
Sprache	englisch
Maße	210 x 279 mm
Gewicht	1294 g
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	A.P. Morse Set Theory • elementary analysis • History of Mathematics • Mathematical Logic and Foundations • measure and integration • set theory
ISBN-10	3-031-05357-5 / 3031053575
ISBN-13	978-3-031-05357-3 / 9783031053573
Zustand	Neuware