Date of Award

January 2021

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Bruce Dearden

Abstract

In the mid 1990s mathematicians Rolando Chuaqui and Patrick Suppes developed a constructive axiomatic system of nonstandard analysis. This project, now called NQA+ (later developed as Elementary Recursive Nonstandard Analysis by Suppes and Richard Sommer) is notable because it has a finitary consistency proof with which we can develop a large fragment of infinitesimal analysis, which they claim represents the mathematical practice characteristic of physics in a manner that does justice to the geometric intuition that facilitated, for example, 17th century indivisible methods. In this thesis I develop the authors’ formulation of geometric subdivision and of the integral as a nonstandard Riemann sum, and provide examples which clarify my main research questions, which are 1) to which practices does geometric subdivision refer? 2) what are their motivations? 3) how does geometric subdivision provide a foundation for NQA+, and what consequences does it have for the continuum of real numbers?

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