Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1981-0609664-9
MathSciNet review: 609664
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03D60, 03D25, 03E15

Retrieve articles in all journals with MSC: 03D60, 03D25, 03E15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0609664-9
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

American Mathematical Society