The term "Godel machine" describes a hypothetical artificial intelligence system that is capable of self-improvement indefinitely. While this specific term may not have many synonyms, there are related terms that describe similar concepts. For example, "artificial superintelligence" refers to a machine that surpasses human intelligence, while "hyperintelligence" refers to intelligence beyond the human level. Additionally, "recursive self-improvement" describes a machine that is capable of improving its own design and functionality. These related terms all explore the potential for machines to exceed human abilities and continuously improve themselves, similar to the theoretical capabilities of a Godel machine.