- 科学基礎論研究 (ISSN:00227668)
- vol.41, no.2, pp.93-101, 2014-03-30 (Released:2017-08-31)
Rosser's provability predicates were introduced by Rosser to improve Godel's first incompleteness theorem. First, we survey the research on Rosser's provability predicates developed by Guaspari and Solovay, and Arai. Secondly, we investigate the formalization of existential version of Yablo's paradox based on Rosser's provability predicates, and show that this formalization can give independednt sentences for any consistent theory. At last, we prove that there is a consistency statement defined by using Rosser's provability predicate, which cannot be proved in arithmetic.