Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 74, Issue 3 (2009), 1047-1060.
Intrinsic bounds on complexity and definability at limit levels
We show that for every computable limit ordinal α, there is a computable structure 𝒜 that is Δα⁰ categorical, but not relatively Δα⁰ categorical (equivalently, it does not have a formally Σα⁰ Scott family). We also show that for every computable limit ordinal α, there is a computable structure 𝒜 with an additional relation R that is intrinsically Σα⁰ on 𝒜, but not relatively intrinsically Σα⁰ on 𝒜 (equivalently, it is not definable by a computable Σα formula with finitely many parameters). Earlier results in , , and  establish the same facts for computable successor ordinals α.
J. Symbolic Logic Volume 74, Issue 3 (2009), 1047-1060.
First available in Project Euclid: 16 June 2009
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Chisholm, John; Fokina, Ekaterina B.; Goncharov, Sergey S.; Harizanov, Valentina S.; Knight, Julia F.; Quinn, Sara. Intrinsic bounds on complexity and definability at limit levels. J. Symbolic Logic 74 (2009), no. 3, 1047--1060. doi:10.2178/jsl/1245158098. https://projecteuclid.org/euclid.jsl/1245158098