Feedback hyperjump-Reference-Cited by-同舟云学术

Feedback hyperjump

Published:2021-01 Issue:1 Volume:31 Page:20-39
ISSN:0955-792X
Container-title:Journal of Logic and Computation
language:en
Short-container-title:

Author:

Aguilera Juan P¹,Lubarsky Robert S²

Affiliation:

1. Department of Mathematics, Ghent University, 9000 Ghent, Belgium, Institute of Discrete Mathematics and Geometry, Vienna University of Technology, 1040 Vienna, Austria

2. Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA

Abstract

Abstract Feedback is oracle computability when the oracle consists exactly of the con- and divergence information about computability relative to that same oracle. Here we study two possible feedback hyperjumps and characterize each of them as the complete $\varSigma _1$ set relative to a level of Gödel’s constructible hierarchy $L$.

Publisher

Oxford University Press (OUP)

Subject

Logic,Hardware and Architecture,Arts and Humanities (miscellaneous),Software,Theoretical Computer Science

Link

http://academic.oup.com/logcom/article-pdf/31/1/20/36677502/exaa085.pdf

Reference18 articles.

1. Feedback Turing computability, and Turing computability as feedback;Ackerman,2015

2. An introduction to feedback Turing computability;Ackerman;Journal of Logic and Computation,2020

3. A characterization of ${\varSigma }_1^1$-reflecting ordinals;Aguilera

4. Rudiments of $\mu $-calculus;Arnold,2001

5. Perspectives in Mathematical Logic;Barwise,1975

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1. Higher-Order Feedback Computation;Lecture Notes in Computer Science;2024

2. Locally hyperarithmetical induction;Bulletin of the London Mathematical Society;2022-11-29

3. A characterization of Σ11-reflecting ordinals;Annals of Pure and Applied Logic;2021-12