Splitting recursively enumerable subalgebras in recursive Boolean algebras |
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Authors: | Shi Niandong |
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Institution: | (1) Department of Mathematics, Nanjing Normal University, Nanjing, China |
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Abstract: | A Boolean algebraB=
is recursive ifB is a recursive subset of ω and the operations Λ, v and ┌ are partial recursive. A subalgebraC ofB is recursive an (r.e.) ifC is a recursive (r.e.) subset of B. Given an r.e. subalgebraA, we sayA can be split into two r.e. subalgebrasA
1 andA
2 if (A
1 ∪A
2)*=A andA
1 ∩A
2={0, 1}. In this paper we show that any nonrecursive r.e. subalgebra ofB can be split into two nonrecursive r.e. subalgebras ofB. This is a natural analogue of the Friedberg's splitting theorem in ω recursion theory. |
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Keywords: | |
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