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arXiv · 1704.01662

A Higher Bachmann-Howard Principle

Anton Freund
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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 $Π^1_1$-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.

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Anton Freund. 2018-09-19. A Higher Bachmann-Howard Principle. https://arxiv.org/abs/1704.01662

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