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Joseph A. Sgro (born September 20, 1949, San Diego, California) is a mathematician, neurologist / neurophysiologist, and an engineering technologist / entrepreneur in the field of frame grabbers, high-speed cameras, smart cameras, image processors, and related computer vision and machine vision technologies. Sgro began his career as an academic researcher in advanced mathematics and logic. He received an AB in Mathematics in 1970 from UCLA followed by an MA in mathematics in 1973 and a PhD in mathematics in 1975 from the University of Wisconsin, where he studied mathematical logic under H. Jerome Keisler〔Mathematics Genealogy Project entry for (Joseph A. Sgro ).〕 who along with Jon Barwise and Kenneth Kunen formed his doctoral committee. After serving as an instructor and post doctoral fellow at Yale and also holding a membership at the Institute for Advanced Studies at Princeton, New Jersey, Sgro returned to school to study neurology, and received his M.D. in 1980 from the Ph.D to M.D. Program of the Leonard M. Miller School of Medicine at the University of Miami, followed by an internal medicine internship at UNC Memorial Hospital, residency in neurology, a fellowship, and faculty position in clinical neurophysiology at the Neurological Institute of New York. As an outgrowth of his work in neurophysiology, while still working as a post-doctoral fellow and an assistant professor of neurology, Sgro founded (Alacron, Inc. ) (formerly Corteks, Inc.until 1990) in 1985 to manufacture technologies relevant to his neurological research. In 1989 he commercialized this technology and began developing array processors, frame grabbers, vision processors, and most recently supported advances in BSI sensor technology. Extending his work in machine vision technology, in 2002, Sgro founded (FastVision, LLC ), a maker of smart cameras, as a subsidiary of Alacron, Inc . ==Mathematical Research== During his first year as a PhD candidate at the University of Wisconsin, Sgro proved that a topological extension of first-order logic using the open set logic quantifier has logical completeness, which had previously been widely believed but had not been proven. Sgro’s proof drew attention throughout mathematical world, and, in 1974, a year before finishing his PhD, he was awarded an appointment as a Josiah Willard Gibbs Instructor in Mathematics at Yale University, received an NSF research grant to continue his work in topological model theory.〔"Topological Model Theory," (National Science Foundation, Division of Mathematical Sciences, award number 77-04131 ), 1977〕 Yale allowed him to accept this honor while remotely completing his thesis and dissertation at Wisconsin, which he did in 1975. His conclusions regarding the topological model theory formed the basis of his PhD thesis and dissertation. During the 1976-1977 academic year Sgro received a Centennial Fellowship〔Centennial Fellowship (Overview and Roster )〕 from the AMS. His work also resulted in an invitation to speak at the Logica Colloquim ’77 European Meeting of the Association for Symbolic Logic. This event was held in Wrocław, Poland, which was then still part of the Eastern Bloc, making Sgro among the first mathematicians from the West to speak at an event “behind the Iron Curtain.”〔Logic Colloquium ’77, Wroclaw, Poland. Macintyre, A., L. Pacholski, J. Paris, eds. In Studies in Logic and the Foundations of Mathematics, Volume 96. Barwise, J., D. Kaplan, H. J. Keisler, et al., series eds. North-Holland Publishing Company, 1978. ISBN 0-444-85178-X.〕 Sgro also spent 1977-1978 at the Institute for Advanced Study at Princeton University.〔Institute for Advanced Study membership roster entry for (Joseph A. Sgro ).〕 Published in 1977, Sgro’s thesis “Completeness Theorems for Topological Models” and extensions of this research including the axiomatization and completeness of continuous functions on product topology open set quantifiers was published in 1976 in the Israel Journal of Mathematics.〔(Completeness theorems for continuous functions and product topologies )〕 Following these results, Sgro published a proof that an extension of the open set quantifier logic using interior operator quantifier logic has completeness and satisfies Craig interpolation.〔(The interior operator logic and product topologies )〕 He further showed that the Souslin-Kleene closure〔(Axioms for abstract model theory )〕 of the open set quantifier logic fails Craig Interpolation which implies that it is strictly weaker than the interior operator logic.〔(Interpolation fails for the Souslin-Kleene closure of the open-set quantifier logic )〕 His later research concentrated on proving the existence of maximal extensions of first order logic which satisfy Łoś's theorem on ultraproducts and have the Souslin-Kleene property.〔(Maximal Logics )〕 Also this was extended to ultraproduct extensions of first order logic which satisfied both the Łoś's theorem and an extended form of the compactness theorem.〔(Ultraproduct invariant logic )〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Joseph Sgro」の詳細全文を読む スポンサード リンク
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