A countable basis for $\Sigma ^{1}_{2}$ sets and recursion theory on $\aleph _{1}$
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- by Wolfgang Maass PDF
- Proc. Amer. Math. Soc. 82 (1981), 267-270 Request permission
Abstract:
Countably many ${\aleph _1}$-recursively enumerable sets are constructed from which all the ${\aleph _1}$-recursively enumerable sets can be generated by using countable union and countable intersection. This implies under $V = L$ that there exists as well a countable basis for $\sum _n^1$ sets of reals, $n \geqslant 2$. Further under $V = L$ the lattice $\mathcal {E}*({\aleph _1})$ of ${\aleph _1}$-recursively enumerable sets modulo countable sets has only ${\aleph _1}$ many automorphisms.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 267-270
- MSC: Primary 03D60; Secondary 03D25, 03E15
- DOI: https://doi.org/10.1090/S0002-9939-1981-0609664-9
- MathSciNet review: 609664