RESIDUAL SETS OF N

Eurides Alves de OLIVEIRA[1]

Mário Tourasse TEIXEIRA IRA¹

§ ABSTRACT: Let R be the class of residual sets of N. For any m e N, R_m Ì R is a Boolean subalgebra modulo m. The family whose members are R_m, m Î N, and whose morfisms are j_m: R_{m ®} R have R as its direct limit. Let d Ì R be the free Boolean algebra with a countable set of generators, d is the direct limit when m = 2ⁿ.

§ KEYWORDS: Residual sets; Boolean algebra; direct limit.

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[1] Departamento de Matemática –Instituto de Geociências e Ciências Exatas - UNESP – 13500-230 – Rio Claro – SP.