Notre Dame Journal of Formal Logic

Strange Structures from Computable Model Theory

Howard Becker

Abstract

Let $L$ be a countable language, let ${\mathcal{I}}$ be an isomorphism-type of countable $L$-structures, and let $a\in2^{\omega}$. We say that ${\mathcal{I}}$ is $a$-strange if it contains a computable-from-$a$ structure and its Scott rank is exactly $\omega_{1}^{a}$. For all $a$, $a$-strange structures exist. Theorem (AD): If $\mathcal{C}$ is a collection of $\aleph_{1}$ isomorphism-types of countable structures, then for a Turing cone of $a$’s, no member of $\mathcal{C}$ is $a$-strange.

Article information

Source
Notre Dame J. Formal Logic, Volume 58, Number 1 (2017), 97-105.

Dates
Received: 21 July 2013
Accepted: 23 March 2014
First available in Project Euclid: 17 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1479351686

Digital Object Identifier
doi:10.1215/00294527-3767941

Mathematical Reviews number (MathSciNet)
MR3595343

Zentralblatt MATH identifier
06686419

Citation

Becker, Howard. Strange Structures from Computable Model Theory. Notre Dame J. Formal Logic 58 (2017), no. 1, 97--105. doi:10.1215/00294527-3767941. https://projecteuclid.org/euclid.ndjfl/1479351686

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