PP-2019-06: Shavrukov, V. Yu. (2019) R.e. prime powers and total rigidity. [Pre-print]
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Abstract
We introduce r.e. prime powers as the least common multiple of the recursive ultrapowers of N of Hirschfeld and the r.e. ultrapowers of N of Hirschfeld & Wheeler. R.e. prime powers help us with establishing that r.e. ultrapowers admit no non-identity self-embeddings, settling an issue raised by Hirschfeld & Wheeler. This parallels an earlier theorem by McLaughlin for recursive ultrapowers.
The road to solution takes us through a number of variants of recursive/online forest colouring tasks. Along the way we also take a look at a Rudin–Keisler-like category of prime filters in the lattice of r.e. sets and discover some r.e. prime powers that do admit non-trivial self-embeddings.
| Item Type: | Pre-print |
|---|---|
| Report Nr: | PP-2019-06 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2019 |
| Subjects: | Logic Mathematics |
| Depositing User: | Dr Marco Vervoort |
| Date Deposited: | 28 Feb 2019 21:47 |
| Last Modified: | 28 Feb 2019 21:47 |
| URI: | https://eprints.illc.uva.nl/id/eprint/1666 |
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