English Dictionary

Rosser's trick

固有名詞

(mathematics) A method for proving Gödel's incompleteness theorems without the assumption that the theory being considered is ω-consistent. While Gödel's original proof uses a sentence that states (informally) "This sentence is not provable", Rosser's trick uses a formula that says "If this sentence is provable, there is a shorter proof of its negation".

日本語の意味

(数学) 「Rosser's trick」は、ω‐整合性を前提とせずにゲーデルの不完全性定理を証明するための方法です。ゲーデルの元の証明が「この文は証明されない」と述べる文を用いるのに対して、Rosserの手法は「もしこの文が証明されるなら、その否定のより短い証明が存在する」という文を用いる点が特徴です。

In his refinement of Gödel's argument, Rosser's trick constructs a sentence asserting that if it were provable then there would be a shorter proof of its negation, avoiding the need for ω-consistency.

ゲーデルの議論を改良したロッサーの手法は、もしその文が証明可能であればその否定により短い証明が存在すると主張する文を構成し、ω整合性の仮定を不要にします。

意味（1）

(mathematics) A method for proving Gödel's incompleteness theorems without the assumption that the theory being considered is ω-consistent. While Gödel's original proof uses a sentence that states (informally) "This sentence is not provable", Rosser's trick uses a formula that says "If this sentence is provable, there is a shorter proof of its negation".