
TL;DR
This paper explores the limits of computability of isomorphisms between copies of certain ordinals using forcing and set-theoretic assumptions, revealing deep connections between logic, set theory, and computability.
Contribution
It demonstrates that for many ordinals, isomorphisms are not computable in the join of certain descriptive set-theoretic sets, under various set-theoretic assumptions.
Findings
Existence of non-computable isomorphisms for ordinals in a club subset of ω₁.
Under V=L, this non-computability result is nearly optimal.
Assuming large cardinals, similar non-computability results extend to all projective functions.
Abstract
We use forcing over admissible sets to show that, for every ordinal in a club , there are copies of such that the isomorphism between them is not computable in the join of the complete set relative to each copy separately. Assuming , this is close to optimal; on the other hand, assuming large cardinals the same (and more) holds for every projective functional.
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.
Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Limits and Structures in Graph Theory
