Number Theory

   

The Q-Universe: A Set Theoretic Construction

Authors: Wes Hansen

In an earlier paper, “The Q-Naturals: A Recursive Arithmetic Which Extends the ‘Standard’ Model,” we developed a set of non-standard naturals called q-naturals and demonstrated, by construction, the existence of a recursive arithmetical structure which extends the “standard” model. In this paper we extend the q-naturals out to algebraic closure and explore the properties of the various sub-structures along the way. In the process of this development, we realize that the “standard” model of arithmetic and the Q-Natural model are simply the zeroth-order and first-order recursive arithmetics, respectively, in a countable subsumption hierarchy of recursive arithmetics; there exist countably many recursive arithmetical structures.

Comments: 105 Pages.

Download: PDF

Submission history

[v1] 2017-07-11 17:00:37
[v2] 2017-08-05 15:40:50
[v3] 2018-06-12 14:09:45

Unique-IP document downloads: 43 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus