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A note on recursive completions of the countable atomless Boolean algebras |
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| Authors: | E W Madison |
| Institution: | (1) Department of Methematics, The University of Iowa, Iowa City, IA 52242, USA |
| Abstract: | The Baire category theorem for compact Hausdorff spaces is used to show that any recursive completion ℬϕof the countable atomless Boolean algebra ℬ is ℬrecursively closed." Also, a theorem of R.D. Anderson on the simplicity of Aut(ℬ) is used to show that uncountably many automorphisms of ℬ extend to ℬϕ. This revised version was published online in June 2006 with corrections to the Cover Date. |
| Keywords: | Cantor space Recursive completion atomless Boolean algebra recursive automorphism admissible indexing regular open sets recursive open sets meager set r e sequences recursively regular open sets recursively closed Baire category theorem |
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