Some new computable structures of high rank

2016/06/02 by Harrison-Trainor, Matthew, Igusa, Gregory, Knight, Julia F.
#03C57 #03D45 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1606.00900

Abstract

We give several new examples of computable structures of high Scott rank. For earlier known computable structures of Scott rank ω₁^CK, the computable infinitary theory is ℵ₀-categorical. Millar and Sacks asked whether this was always the case. We answer this question by constructing an example whose computable infinitary theory has non-isomorphic countable models. The standard known computable structures of Scott rank ω₁^CK+1 have infinite indiscernible sequences. We give two constructions with no indiscernible ordered triple.

Related

• Structures in Familiar Classes Which Have Scott Rank ω₁^CK
• Scott ranks of models of a theory
• Computable structures of rank omega₁^CK
• The structural complexity of models of arithmetic
• Model Theoretic Complexity of Automatic Structures