A Higher Bachmann-Howard Principle
Abstract
We present a higher well-ordering principle which is equivalent (over Simpson's set theoretic version of ) to the existence of transitive models of Kripke-Platek set theory, and thus to -comprehension. This is a partial solution to a conjecture of Montalb\'an and Rathjen: partial in the sense that our well-ordering principle is less constructive than demanded in the conjecture.
Keywords
Cite
@article{arxiv.1704.01662,
title = {A Higher Bachmann-Howard Principle},
author = {Anton Freund},
journal= {arXiv preprint arXiv:1704.01662},
year = {2018}
}
Comments
This paper is no longer up to date: It is superseded by the author's PhD thesis (available at http://etheses.whiterose.ac.uk/20929/) and the streamlined presentation in arXiv:1809.06759. In contrast to the present abstract, we have now found a computable version of our well-ordering principle. Thus the conjecture by Montalb\'an and Rathjen can be considered as fully solved