Set Theory and Logic


Confirmation of the Collapse of the Buss Hierarchy of Bounded Arithmetics

Authors: Colin James III

Two seminal rules of inference evaluated as not tautologous. This means the following are also refuted: Buss’s hierarchy of bounded arithmetics does not entirely collapse; Takeuti’s argument implies P ≠ NP; and systems PV and PV−. What follows is that separation of bounded arithmetic using a consistency statement is not viable. Therefore the above are non tautologous fragments of the universal logic VŁ4.

Comments: Pages.

Download: PDF

Submission history

[v1] 2019-04-16 17:41:49

Unique-IP document downloads: 15 times 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. 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