PP-2019-06: R.e. prime powers and total rigidity

PP-2019-06: Shavrukov, V. Yu. (2019) R.e. prime powers and total rigidity. [Pre-print]

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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
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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