The Order of Reflection

DOI10.1017/JSL.2021.3arXiv1906.11769MaRDI QIDQ6321168

Juan P. Aguilera

Publication date: 27 June 2019

Abstract: Extending Aanderaa's classical result that $p{i}_1^1<sigm{a}_1^1$, we determine the order between any two patterns of iterated $Sigm{a}_1^1$- and $P{i}_1^1$-reflection. We show that this emph{linear reflection order} is a prewellordering of length $omeg{a}^{o}mega$. This requires considering the relationship between linear and some emph{non-linear} reflection patterns, such as $sigm{a}_1^{1}wedgep{i}_1^1$, the pattern of simultaneous $Sigm{a}_1^1$- and $P{i}_1^1$-reflection.

Mathematics Subject Classification ID

Inner models, including constructibility, ordinal definability, and core models (03E45) Word problems, etc. in computability and recursion theory (03D40) Ordinal and cardinal numbers (03E10) Computability and recursion theory on ordinals, admissible sets, etc. (03D60)

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