Notre Dame Journal of Formal Logic

Strange Structures from Computable Model Theory

Howard Becker

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Abstract

Let L be a countable language, let I be an isomorphism-type of countable L-structures, and let a2ω. We say that I is a-strange if it contains a computable-from-a structure and its Scott rank is exactly ω1a. For all a, a-strange structures exist. Theorem (AD): If C is a collection of 1 isomorphism-types of countable structures, then for a Turing cone of a’s, no member of 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

Subjects
Primary: 03C57: Effective and recursion-theoretic model theory [See also 03D45]
Secondary: 03D45: Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55] 03E60: Determinacy principles

Keywords
Scott rank computable structures axiom of determinacy

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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