On sequences generic in the sense of Prikry

A. R. D. Mathias

doi:10.1017/S1446788700028755

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I establish here a criterion for a sequence of ordinals to be generic over a transitive model of ZFC with respect to a notation of forcing first considered by Prikry in his Doctoral dissertation [2]. In Section 0 I review some notation, in Section 1 I list some facts about measurable cardinals, and in Section 2, after giving Prikry's result, I state and prove mine.

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[1]Jensen, R. B., Modelle der Mengenlehre (Springer-Verlag, Lecture Notes Series, 1968).Google Scholar

[2]Prikry, K. L., Doctoral dissertation (Berkeley, 1968). Published as ‘Changing measurable into accessible cardinals’ in Dissertationes Math. (Rozprawy Mat.) 68 (1969).Google Scholar

[3]Solovay, R. M., ‘Real-valued measurable cardinals,’ in the Proceedings of the 1967 Summer Institute in Set Theory held at Los Angeles.Google Scholar

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On sequences generic in the sense of Prikry

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