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A countable basis for $ \Sigma \sp{1}\sb{2}$ sets and recursion theory on $ \aleph \sb{1}$

Author: Wolfgang Maass
Journal: Proc. Amer. Math. Soc. 82 (1981), 267-270
MSC: Primary 03D60; Secondary 03D25, 03E15
MathSciNet review: 609664
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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.

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Keywords: $ \alpha $-recursively enumerable sets, automorphisms of r.e. sets, countable unions and intersections of $ \sum _2^1$-sets
Article copyright: © Copyright 1981 American Mathematical Society

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