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Autostability of hyperarithmetical models

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Abstract

Let\(\mathfrak{M}\) be a Δ 11 -constructivizable model. If its Scott rank\(sr(\mathfrak{M})\) is strictly less than ω CK1 , then it is proved autostable. But if\(sr(\mathfrak{M}) = \omega _1^{CK} \), then there exists an ordinal α<ω CK1 for which\(\mathfrak{M}\) is not autostable in any degree O(γ+1) for all γ>α. We also consider some problems concerning Δ 11 -autostability of Δ 11 -constructivizable Boolean algebras.

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Authors
  1. A. V. Romina
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Additional information

Supported through the FP “Integration” and the RP “Universities of Russia. Fundamental Research.”

Translated fromAlgebra i Logika, Vol. 39, No. 2, pp. 198–205, March–April, 2000.

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Romina, A.V. Autostability of hyperarithmetical models. Algebr Logic 39, 114–118 (2000). https://doi.org/10.1007/BF02681665

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  • DOI: https://doi.org/10.1007/BF02681665

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