Аннотация
We study computable reducibility of computable metrics on R induced by reducibility of their respective Cauchy representations. It is proved that this ordering has a subordering isomorphic to an arbitrary countable tree. Also we introduce a weak version of computable reducibility and construct a countable antichain of computable metrics that are incomparable with respect to it. Informally, copies of the real line equipped with these metrics are pairwise homeomorphic but not computably homeomorphic.
Язык оригинала | английский |
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Страницы (с-по) | 302-317 |
Число страниц | 16 |
Журнал | Algebra and Logic |
Том | 56 |
Номер выпуска | 4 |
DOI | |
Состояние | Опубликовано - 1 сен 2017 |