## On self-embeddings of computable linear orderings.(English)Zbl 1105.03036

The authors prove that there exists a computable linear ordering without nontrivial $${\mathbf 0}^\prime$$-computable self-embeddings. It appeared that the previously published proof of this statement in [S. Lempp, A. Morozov, C. McCoy and D. R. Solomon, “On self-embeddings of computable linear orders”, in: S. B. Cooper et al. (eds.), Computability and models. Kluwer Academic/Plenum Publishers, New York, 259–265 (2003; Zbl 1104.03001)] contains an error. The question of how much computability we need to compute such embeddings in the general case and for various kinds of orderings is also studied.

### MSC:

 03D45 Theory of numerations, effectively presented structures 03C57 Computable structure theory, computable model theory

Zbl 1104.03001
Full Text:

### References:

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