Projects per year
Abstract
The familiar continuum R of real numbers is obtained by a wellknown procedure which, starting with the set of natural numbers N=\omega, produces in a canonical fashion the field of rationals Q and, then, the field R as the completion of Q under Cauchy sequences (or, equivalently, using Dedekind cuts). In this article, we replace \omega by any infinite suitably closed ordinal \kappa in the above construction and, using the natural (Hessenberg) ordinal operations, we obtain the corresponding field \kappaR, which we call the field of the \kappareals. Subsequently, we study the properties of the various fields \kappaR and develop their general theory, mainly from the settheoretic perspective. For example, we investigate their connection with standard themes such as forcing and descriptive set theory.
Original language  English 

Pages (fromto)  136 
Number of pages  36 
Journal  Journal of Logic and Analysis 
Volume  10 
Issue number  1 
DOIs  
Publication status  Published  1 Oct 2018 
Keywords
 Real numbers
 Hessenberg operations
 Ordered fields
 Forcing
 Descriptive set theory
Projects
 1 Finished

Iterated Forcing with Side Conditions and High Forcing Axioms (DL open)
Engineering and Physical Sciences Research Council
8/08/16 → 7/08/19
Project: Research