Effective Polish space

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In mathematical logic, an effective Polish space is a complete separable metric space that has a computable presentation. Such spaces are studied in effective descriptive set theory and in constructive analysis.

Definition[edit]

An effective Polish space is a complete separable metric space X with metric d such that there is a countable dense set C = (c0, c1,...) that makes the following two relations on \mathbb{N}^4 computable (Moschovakis 2009:142):

P(i,j,k,m) \equiv d(c_i,c_j) \leq \frac{m}{k+1}
Q(i,j,k,m) \equiv d(c_i,c_j) < \frac{m}{k+1}

References[edit]