Construção de Domínios Bi-Scott via Completação por Ideais
DOI:
https://doi.org/10.5540/tema.2007.08.03.0341Abstract
Uma técnica para lidar com domínios não contáveis através de domínios contáveis é usar a noção de completação. Neste artigo, propomos uma representação de domínios bi-Scott (domínios de Scott cuja reversa também é um domínio deScott) via completação por ideais de posets contáveis bi-finitamente consistentemente completos com menor e maior elemento. Mostramos que o construtor intervalar é fechado sobre esta classe de domínios e que funções monotônicas entre estes posets podem ser transformadas (completadas) numa função contínua entre os domínios bi-Scotts representados pelos posets. A partir deste último resultado, podemos obter uma definição básica de computabilidade entre domínios bi-Scott baseada na noção clássica de computabilidade (por exemplo, usando máquinas de Turing) entre seus posets de elementos finitos.References
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