Koiran’s quasiminimality question for unary entire functions
For every entire function , is every subset of definable, with parameters, in the structure either countable or co-countable?
References
Primary source
Additional references
- An entire function that violates quasiminimality — arXiv — Spencer Dembner
Progress summary
A new preprint claims to disprove the proposed extension of quasiminimality to all unary entire functions, but the result has not been independently checked.
Koiran asked whether expanding the complex field by all unary entire functions is quasiminimal. Earlier literature described this as open and harder than the corresponding group case.
Known results
- Kirby, 2023: recorded Koiran’s question and Wilkie’s observation that no counterexample was known.
- Dmitrieva, 2025: proved quasiminimality for selected analytic expansions, but not for arbitrary unary entire functions.
- A 2023 account stated that it remained unknown whether even one unary entire function could yield a non-quasiminimal expansion.
October 2026 counterexample
Spencer Dembner’s preprint claims to construct, using holomorphic approximation, a unary entire function whose expansion is not quasiminimal, thereby answering Koiran’s question negatively. The claim is currently unverified.
Current status (as of October 2026): A preprint claims a counterexample that would settle the question negatively, but independent verification is absent, so the resolution remains unconfirmed.
Sources
- arxiv.org
- ar5iv.labs.arxiv.org
- ueaeprints.uea.ac.uk
- arxiv.org
- arxiv.org
- homepages.math.uic.edu
- ncatlab.org
- openai.com
- digital.lib.washington.edu
- cdn.openai.com
- ar5iv.labs.arxiv.org
- ar5iv.labs.arxiv.org
- arxiv.org
- export.arxiv.org
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
Solutions 0
No solutions have been posted yet.