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arXiv · 1906.11769

The Order of Reflection

J. P. Aguilera
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Abstract

Extending Aanderaa's classical result that $π^1_1<σ^1_1$, we determine the order between any two patterns of iterated $Σ^1_1$- and $Π^1_1$-reflection. We show that this \emph{linear reflection order} is a prewellordering of length $ω^ω$. This requires considering the relationship between linear and some \emph{non-linear} reflection patterns, such as $σ^1_1\wedgeπ^1_1$, the pattern of simultaneous $Σ^1_1$- and $Π^1_1$-reflection.

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J. P. Aguilera. 2019-06-27. The Order of Reflection. https://doi.org/10.1017/jsl.2021.3

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