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STRUCTURAL HIGHNESS NOTIONS

Part of: Model theory Computability and recursion theory

Published online by Cambridge University Press:  28 April 2022

WESLEY CALVERT Open the ORCID record for WESLEY CALVERT [Opens in a new window] ,
JOHANNA N. Y. FRANKLIN Open the ORCID record for JOHANNA N. Y. FRANKLIN [Opens in a new window]  and
DAN TURETSKY
WESLEY CALVERT*
Affiliation:
SCHOOL OF MATHEMATICAL AND STATISTICAL SCIENCES SOUTHERN ILLINOIS UNIVERSITY MAIL CODE 4408, 1245 LINCOLN DRIVE CARBONDALE, IL 62901, USA URL: http://lagrange.math.siu.edu/calvert
JOHANNA N. Y. FRANKLIN
Affiliation:
DEPARTMENT OF MATHEMATICS HOFSTRA UNIVERSITY ROOM 306, ROOSEVELT HALL HEMPSTEAD, NY 11549-0114, USA E-mail: johanna.n.franklin@hofstra.edu URL: http://www.johannafranklin.net
DAN TURETSKY
Affiliation:
SCHOOL OF MATHEMATICS AND STATISTICS VICTORIA UNIVERSITY OF WELLINGTON WELLINGTON, NEW ZEALAND E-mail: dan.turetsky@vuw.ac.nz
*
E-mail: wcalvert@siu.edu
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Abstract

We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and several other problems related to computing isomorphisms. These other problems include Scott analysis (in the form of back-and-forth relations), jump hierarchies, and computing descending sequences in linear orders.

Keywords

highness for isomorphismScott rankHarrison orderingsjump hierarchiestraceability

MSC classification

Primary: 03C57: Effective and recursion-theoretic model theory
Secondary: 03D28: Other Turing degree structures 03D45: Theory of numerations, effectively presented structures

Information

Type
Article
Information
The Journal of Symbolic Logic , Volume 88 , Issue 4 , December 2023 , pp. 1692 - 1724
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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