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Intrinsic bounds on complexity and definability at limit levels

  • John Chisholm (a1), Ekaterina B. Fokina (a2), Sergey S. Goncharov (a3), Valentina S. Harizanov (a4), Julia F. Knight (a5) and Sara Quinn (a6)...
Abstract

We show that for every computable limit ordinal α, there is a computable structure that is categorical, but not relatively categorical (equivalently, it does not have a formally Scott family). We also show that for every computable limit ordinal α, there is a computable structure with an additional relation R that is intrinsically on , but not relatively intrinsically on (equivalently, it is not definable by a computable Σα formula with finitely many parameters). Earlier results in [7], [10], and [8] establish the same facts for computable successor ordinals α.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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