David Marker : Integer Parts of Uncountable Real Closed Fields

Posted by David E. Marker , part of the Logic Seminar.

At

Aug. 28, 2012, 4 p.m.

In

SEO 427

Abstract

An integer part of a real closed field is a discretely ordered subring where every element of the field is within distance one of an element of the ring. Sheperdson first noticed that integer parts are models of a weak fragment of arithmetic. Recently, D'Aquino, Knight and Starchenko studied the real closed fields where the integer part is a model of Peano Arithmentic and gave a complete classification in the countable case. We will survey the subject and examine some phenomena in the uncountable case.