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Arithmetical hierarchy

In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy (after mathematicians Stephen Cole Kleene and Andrzej Mostowski) classifies certain sets based on

Arithmetical set

In mathematical logic, an arithmetical set (or arithmetic set) is a set of natural numbers that can be defined by a formula of first-order Peano arithmetic. The arithmetical sets are classified by the

Analytical hierarchy

In mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy. The analytical hierarchy of formulas includes formulas in the language of seco

Lightface analytic game

In descriptive set theory, a lightface analytic game is a game whose payoff set A is a subset of Baire space; that is, there is a tree T on which is a computable subset of , such that A is the project

Effective Polish space

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

Effective descriptive set theory

Effective descriptive set theory is the branch of descriptive set theory dealing with sets of reals having lightface definitions; that is, definitions that do not require an arbitrary real parameter (

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