Saturation properties of ideals in generic extensions. II

Authors:
James E. Baumgartner and Alan D. Taylor

Journal:
Trans. Amer. Math. Soc. **271** (1982), 587-609

MSC:
Primary 03C62; Secondary 03E05, 03E35, 03E40, 03E55

DOI:
https://doi.org/10.1090/S0002-9947-1982-0654852-4

MathSciNet review:
654852

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Abstract: The general type of problem considered here is the following. Suppose is a countably complete ideal on satisfying some fairly strong saturation requirement (e.g. is precipitous or -saturated), and suppose that is a partial ordering satisfying some kind of chain condition requirement (e.g. has the c.c.c. or forcing with preserves ). Does it follow that forcing with preserves the saturation property of ? In this context we consider not only precipitous and -saturated ideals, but we also introduce and study a class of ideals that are characterized by a property lying strictly between these two notions. Some generalized versions of Chang's conjecture and Kurepa's hypothesis also arise naturally from these considerations.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1982-0654852-4

Article copyright:
© Copyright 1982
American Mathematical Society