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ASSIGNING AN ISOMORPHISM TYPE TO A HYPERDEGREE

Published online by Cambridge University Press:  10 December 2019

HOWARD BECKER
HOWARD BECKER*
Affiliation:
PMB 128, 4711 FOREST DR., STE. 3 COLUMBIA, SC29206, USAE-mail: hsbecker@hotmail.com
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Abstract

Let L be a computable vocabulary, let XL be the space of L-structures with universe ω and let $f:{2^\omega } \to {X_L}$ be a hyperarithmetic function such that for all $x,y \in {2^\omega }$, if $x{ \equiv _h}y$ then $f\left( x \right) \cong f\left( y \right)$. One of the following two properties must hold. (1) The Scott rank of f (0) is $\omega _1^{CK} + 1$. (2) For all $x \in {2^\omega },f\left( x \right) \cong f\left( 0 \right)$.

Keywords

Primary 03C5703D4503E15Scott rankcomputable structuredescriptive complexity
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 1 , March 2020 , pp. 325 - 337
Copyright
Copyright © The Association for Symbolic Logic 2019 

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