Victor Ocasio : Computability in the class of real closed fields

Posted by Isaac Goldbring , part of the Logic Seminar.

At

Dec. 3, 2013, 4 p.m.

In

SEO 427

Abstract

The class of Real Closed Fields (RCF) is known to have very nice model theoretic properties, among them o-minimality and quantifier elimination. In our work, we consider some non- elementary subclasses of RCF and explore their computability theoretic properties. We locate the class of Archimedean Real Closed Fields using Turing computable embeddings (an analog of Borel embeddings) and compare it with other non-elementary first order subclasses of RCF. We also explore relative categoricity and show that under some conditions one can obtain a sharp result on the complexity of the relative categoricity of a real closed field that is constructed using a linear order as an oracle.