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Chernikov–Hempel conjecture on $k$ -independence of fields
Chernikov–Hempel conjecture. If a field is $k$ -independent for some $k\ge 2$ , then it is $k$ -independent for all $k$ .
Conjectureopenfields independence-properties model-theoryarXiv posted 2 days ago

Chernikov–Hempel conjecture on kkk-independence of fields