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Strong constructibility of Boolean algebras of elementary characteristic (1,1,0). (English. Russian original) Zbl 0824.03018
Algebra Logic 32, No. 6, 334-341 (1993); translation from Algebra Logika 32, No. 6, 618-630 (1993).
The paper contains a step in the solution of the problem formulated by S. P. Odintsov [“Restricted theories of constructive Boolean algebras in the lower layer”, Inst. Mat., Novosibirsk, Prepr. No. 12 (1986)]: does there exist a constructive but not strongly constructivizable Boolean algebra of the Ershov-Tarski characteristic (1,1,0) admitting a constructivization with a recursive set of atoms? The result is the following Theorem. If a constructive Boolean algebra $$\langle B, \nu\rangle$$ of the Ershov-Tarski characteristic (1,1,0) has a recursive set of atoms and is effectively presented as a direct sum of constructive Boolean algebras $$\langle B_ i, \nu_ i\rangle$$ with the first characteristic 0, then $$B$$ is strongly constructivizable. To solve this problem completely, now it would be good to find some effective representation for any constructive Boolean algebra with recursive set of atoms.

##### MSC:
 03D45 Theory of numerations, effectively presented structures 06E99 Boolean algebras (Boolean rings)
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##### References:
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