A Higher Bachmann-Howard Principle

Abstract

We present a higher well-ordering principle which is equivalent (over Simpson's set theoretic version of ${\text{ATR}}_0$) to the existence of transitive models of Kripke-Platek set theory, and thus to ${\Pi }_1^1$-comprehension. This is a partial solution to a conjecture of Montalbán and Rathjen: partial in the sense that our well-ordering principle is less constructive than demanded in the conjecture.

arXiv commentThis paper is no longer up to date: It is superseded by the author's PhD thesis (available at http://etheses.whiterose.ac.uk/20929/) and the streamlined presentation in arXiv:1809.06759.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 Montalbán and Rathjen can be considered as fully solved

Cited by in corpus (3)

• ${\Pi }_1^1$-Comprehension as a Well-Ordering Principle
• A Categorical Construction of Bachmann-Howard Fixed Points
• Set-theoretic reflection is equivalent to induction over well-founded classes