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Kajitori, Kazuaki 2014-12-16T06:18:16Z 2014-12-16T06:18:16Z 10000-01-01 1986 1986 The subject of the thesis is precipitous ideals on complete Boolean algebras (abbr. cBas) which are generalizations of precipitous ideals on power sets introduced by Jech and Prikry. Various results on the original notion are generalized to the case of cBas, some by using a new tool (the sum operation of ideals on cBas introduced by J. Takahashi). Among those are: consistency strength of the existence of a precipitous ideal on a cBa (being that of a measurable); precipitousness of a (kappa)-complete (kappa)('+)-saturated ideal on a cBa; a game-theoretic characterization of the precipitousness; preservation theorems for precipitousness under Boolean extension. Some results cannot be generalized. For example, it is shown that there is no (kappa)('+)-saturated (kappa)-complete ((kappa)('+)-incomplete) ideal on a (kappa)-collapsing algebra. Also, it is shown, in analogy to an algebraic characterization of a compact cardinal, that it is consistent (modulo a compact cardinal) that every (kappa)-complete ideal on a ((kappa),(INFIN))-distributive cBa has a (kappa)-complete precipitous extension. Made available in DSpace on 2014-12-16T06:18:16Z (GMT). No. of bitstreams: 1 8701520.pdf: 2639834 bytes, checksum: a77baa0dd49e4855d747e5fa6842b71f (MD5) Previous issue date: 1986 Embargo set by: Seth Robbins for item 71409 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 99 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1986. http://hdl.handle.net/2142/71243 (UMI)AAI8701520 Mathematics Precipitous Ideals on Cbas (Complete Boolean Algebras) text Ph.D. Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation