In mathematical logic, Rosser's trick is a method for proving a variant of Gödel's incompleteness theorems not relying on the assumption that the theory being considered is ω-consistent Wikipedia

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 says (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". Wiktionary