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Wikipedia definition
1. Ω-consistent theoryIn mathematical logic, an ω-consistent (or omega-consistent, also called numerically segregative) theory is a theory that is not only (syntactically) consistent (that is, does not prove a contradiction), but also avoids proving certain infinite combinations of sentences that are intuitively contradictory. The name is due to Kurt Gödel, who introduced the concept in the course of proving the incompleteness theorem.
Read “Ω-consistent theory” on English Wikipedia
Read “Ω無矛盾” on Japanese Wikipedia
Read “Ω-consistent theory” on DBpedia

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