Preprint
Oct 2026
A Reflection Calculus for Bar Induction and the Linearity of Consistency Strength Ordering
We introduce a novel extension of reflection calculus, $\mathsf{RC_{BI}}$, to analyze a family of extensions of $\mathsf{ACA}_0$ generated by uniform $\omega$-model and syntactic reflection principles, together with several other related operators. The union of these theories coincides with the theory of Bar Induction...
F. Pakhomov, Vlad Lazar
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