Structures in Familiar Classes Which Have Scott Rank $\omega_1^{CK}$

Wesley Calvert; Sergey S. Goncharov; Julia F. Knight

Structures in Familiar Classes Which Have Scott Rank $\omega_1^{CK}$

Logic 2008-03-25 v1

Authors: Wesley Calvert , Sergey S. Goncharov , Julia F. Knight

Abstract

There are familiar examples of computable structures having various computable Scott ranks. There are also familiar structures, such as the Harrison ordering, which have Scott rank $\omega_1^{CK}+1$ . Makkai produced a structure of Scott rank $\omega_1^{CK}$ , which can be made computable, and simplified so that it is just a tree. In the present paper, we show that there are further computable structures of Scott rank $\omega_1^{CK}$ in the following classes: undirected graphs, fields of any characteristic, and linear orderings. The new examples share with the Harrison ordering, and the tree just mentioned, a strong approximability property.

Keywords

matrix rank phylogenetic trees simplicial complexes

Cite

@article{arxiv.0803.3296,
  title  = {Structures in Familiar Classes Which Have Scott Rank $\omega_1^{CK}$},
  author = {Wesley Calvert and Sergey S. Goncharov and Julia F. Knight},
  journal= {arXiv preprint arXiv:0803.3296},
  year   = {2008}
}

Comments

Advances in Logic (Proceedings of the North Texas Logic Conference, October 8--10, 2004), Contemporary Mathematics 425 (2007), American Mathematical Society, 49--66

Structures in Familiar Classes Which Have Scott Rank $\omega_1^{CK}$

Abstract

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