A Boolean algebra B=<B,∧,∨,>is recursive if B is a recursive subset of ω and theoperations ∧,∨ and are partial recursive.A subalgebra C of B is recursive an（r.e.）if C is a recursive（r.e.）subset of B.Gi...A Boolean algebra B=<B,∧,∨,>is recursive if B is a recursive subset of ω and theoperations ∧,∨ and are partial recursive.A subalgebra C of B is recursive an（r.e.）if C is a recursive（r.e.）subset of B.Given an r.e.subalgebra A,we say A can be split into two r.e.subalgebras A1and A2if（A1∪A2）=A and A1∩A2={0,1}.In this paper we show that any nonrecursive r.e.subalgebra of B canbe split into two nonrecursive r.e.subalgebras of B.This is a natural analogue of the Friedberg’s splittingtheorem in ω recursion theory.展开更多
文摘A Boolean algebra B=<B,∧,∨,>is recursive if B is a recursive subset of ω and theoperations ∧,∨ and are partial recursive.A subalgebra C of B is recursive an（r.e.）if C is a recursive（r.e.）subset of B.Given an r.e.subalgebra A,we say A can be split into two r.e.subalgebras A1and A2if（A1∪A2）=A and A1∩A2={0,1}.In this paper we show that any nonrecursive r.e.subalgebra of B canbe split into two nonrecursive r.e.subalgebras of B.This is a natural analogue of the Friedberg’s splittingtheorem in ω recursion theory.
