In this paper, we show that for each forcing notion P in a transitive model M of ZFC, if P satisfies some conditions, there is an elementary embedding from M into a generic ultrapower contains a P-generic set. And, we also introduce the result that if we assume the existence of some large cardinals, the above generic ultrapower can be well-founded. Using this result, we prove some theorems on the problems of regularity properties of definable sets of reals.

Background: Respiratory syncytial virus (RSV) is one of the major viruses that cause respiratory infections in all generations, not only in neonates and infants. There is a limited number of reports on serological epidemiology of RSV subgroups A and B. Neutralizing test (NT) antibody reflects protective immunity but bothersome. Sero-epidemiological study should be performed using practical NT method. Methods: Two wild-type viruses subgroups A and B, isolated in 2013, and the Long strain was used as the challenge viruses. NT antibody (...) with 100% inhibition of cytopathic effect (CPE) was examined. A total of 91 serum samples obtained from 0 to 12 years subjects without RSV infection who visited our hospital with some health problems and 121 sera obtained from healthy subjects in different age groups were used. Serological epidemiology of subgroups A and B was investigated in this study using new NT methods. Results: 1) A simple and practical NT method was developed. 2) The NT antibody titer was lowest in <1 year of age (5 × 21.70 ± 2.03 against subgroup A and 5 × 20.85 ± 1.31 against subgroup B) and increased in 3 years of age or older, and high antibody titers were maintained during school age. 3) A slight difference was observed in the NT antibody titers against subgroups A and Bin young children <3 years, but not after 3 years of age, reflecting the repeated infections. 4) Specific IgG antibody against RSV was measured. The IgG EIA values decreased with age. No association was observed between IgG EIA and NT titers. Conclusions: A simple NT assay method was developed in the present study. By the age of 3 years, high NT antibody titers were observed and maintained until 12 years. The IgG (EIA) values decreased with age. No association was observed between IgG (EIA) and NT titers. (shrink)