Extending Properly n-REA Sets
| Autor: | Cholak, Peter A., Gerdes, Peter M. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3233/COM-210362 |
| Popis: | In [5] Soare and Stob prove that if $A$ is an r.e. set which isn't computable then there is a set of the form $A \oplus W^A_e$ which isn't of r.e. Turing degree. If we define a properly $n+1$-REA set to be an $n+1$-REA set which isn't Turing equivalent to any $n$-REA set this result shows that every properly 1-REA set can be extended to a properly 2-REA set. This result was extended in [1] by Cholak and Hinman who proved that every 2-REA set can be extended to a properly 3-REA set. This leads naturally to the hypothesis that every properly $n$-REA set can be extended to a properly $n+1$-REA set. In this paper, we show this hypothesis is false and that there is a properly $3$-REA set which can't be extended to a properly $4$-REA set. |
| Databáze: | arXiv |
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