Proofs, Constructions and Computations research seminars: A cohesive power of N with order type N + Q

Dr Paul Shafer (University of Leeds) will present his research in Proofs, Constructions and Computations.

A cohesive power is an effective analogue of an ultrapower, where the base structure is computable and a cohesive set plays the role of an ultrafilter.  We study the cohesive powers of computable copies of the structure (N, <), i.e., the natural numbers as a linear order.  If one forms the cohesive power of the usual presentation of (N, <), then the resulting linear order has order type N + ZQ (which is familiar as the order type of countable non-standard models of Peano arithmetic).  In contrast to this, we show that there is a computable copy, L, of (N, <) whose cohesive power has order type N + Q.

This work of Dr Paul Shafer is joint with Rumen Dimitrov (Western Illinois University), Valentina Harizanov (George Washington University), Andrey Morozov (Sobolev Institute of Mathematics), Alexandra Soskova (Sofia University), and Stefan Vatev (Sofia University).