English Dictionary

arithmetical hierarchy

名詞

(logic) A hierarchy which classifies the complexity of first-order formulae (and sets defined by them) based on the number of alternations between series of unbounded existential quantifiers and universal quantifiers.

日本語の意味

算術階層：一階述公式やそれによって定義される集合の複雑さを、無制限の存在記号と全称記号が交互に現れる回数に基づいて分類するための論理学的な階層構造。

To determine the descriptive power of different fragments, researchers examine the arithmetical hierarchy, which classifies the complexity of first-order formulas and the sets they define by counting alternations between blocks of unbounded existential and universal quantifiers.

異なる断片の記述力を判断するために、研究者たちは第一階述語論理の式やそれらが定義する集合の複雑さを、非有界の存在量化子と全称量化子のブロックの交替回数によって分類する算術階層を調べる。

意味（1）

(logic) A hierarchy which classifies the complexity of first-order formulae (and sets defined by them) based on the number of alternations between series of unbounded existential quantifiers and universal quantifiers.

arithmetical hierarchies （ plural ）