Logic Seminar-Ultrapower construction of the hyperreals

Time: Thursday, September 15, 11:00 am-12:00 noon

Place: Smith 120

Speaker:  Henry Klatt, GWU

Title: Ultrapower construction of the hyperreals

Abstract: Few stories in the history of mathematics are as dramatic and entertaining as the story of the infinitesimal. Sitting at the center of the historical development of calculus, the topic pits philosophy, intuition, rigor, and computation against one another, along side a rich cast of characters including Isaac Newton, Karl Weierstrass, and Imre Lakatos. In the 1960s, Abraham Robinson placed the infinitesimal system, by then usurped by the more parsimonious Weierstrassian system of limits based on inequalities, on a rigorous footing using the techniques of model theory, creating a completely equivalent and more algebraically flavored approach to calculus. In this talk, we will review the ultrapower construction of the Hyperreals, how the system is used for calculus, and give a brief overview of the system's cultural status.