A countable basis for sets and recursion theory on

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 -recursively enumerable sets are constructed from which all the -recursively enumerable sets can be generated by using countable union and countable intersection. This implies under that there exists as well a countable basis for sets of reals, . Further under the lattice of -recursively enumerable sets modulo countable sets has only many automorphisms.

**[1]***Handbook of mathematical logic*, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Edited by Jon Barwise; With the cooperation of H. J. Keisler, K. Kunen, Y. N. Moschovakis and A. S. Troelstra; Studies in Logic and the Foundations of Mathematics, Vol. 90. MR**0457132****[2]**Manuel Lerman,*Lattices of 𝛼-recursively enumerable sets*, Generalized recursion theory, II (Proc. Second Sympos., Univ. Oslo, Oslo, 1977) Stud. Logic Foundations Math., vol. 94, North-Holland, Amsterdam-New York, 1978, pp. 223–238. MR**516937****[3]**R. Mansfield,*The solution to one of Ulam’s problems concerning analytic sets. II.*, Proc. Amer. Math. Soc.**26**(1970), 539–540. MR**0279265**, 10.1090/S0002-9939-1970-0279265-6**[4]**Robert I. Soare,*Automorphisms of the lattice of recursively enumerable sets. I. Maximal sets*, Ann. of Math. (2)**100**(1974), 80–120. MR**0360235****[5]**Robert I. Soare,*Recursively enumerable sets and degrees*, Bull. Amer. Math. Soc.**84**(1978), no. 6, 1149–1181. MR**508451**, 10.1090/S0002-9904-1978-14552-2**[6]**Robert M. Solovay,*A model of set-theory in which every set of reals is Lebesgue measurable*, Ann. of Math. (2)**92**(1970), 1–56. MR**0265151****[7]**K. Sutner,*Automorphisms of**-recursively enumerable sets*, Diplomarbeit an der Universität München, 1979.

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

Keywords:
-recursively enumerable sets,
automorphisms of r.e. sets,
countable unions and intersections of -sets

Article copyright:
© Copyright 1981
American Mathematical Society