Strong Jump Inversion
W. Calvert, A. Frolov, V. Harizanov, J. Knight, C. McCoy, A. Soskova,, S. Vatev

TL;DR
This paper establishes general conditions under which structures admit strong jump inversion, extending known results to classes like linear orderings, trees, and models of differential fields, with implications for computability and isomorphism complexity.
Contribution
It provides a broad theorem giving sufficient conditions for strong jump inversion, unifying and extending previous results across various classes of structures.
Findings
Boolean algebras with no 1-atom admit strong jump inversion
Models of DCF_0 admit strong jump inversion and have decidable saturated models
The paper offers a computable enumeration of types in models of DCF_0
Abstract
We say that a structure admits \emph{strong jump inversion} provided that for every oracle , if computes for some , then computes for some . Jockusch and Soare \cite{JS} showed that there are low linear orderings without computable copies, but Downey and Jockusch \cite{DJ} showed that every Boolean algebra admits strong jump inversion. More recently, D.\ Marker and R.\ Miller \cite{MM} have shown that all countable models of (the theory of differentially closed fields of characteristic ) admit strong jump inversion. We establish a general result with sufficient conditions for a structure to admit strong jump inversion. Our conditions involve an enumeration of -types, where these are made up of formulas that are Boolean combinations of…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
