On a combinatorial property of menas related to the partition property for measures on supercompact cardinals
| Autor: | Kenneth Kunen, Donald H. Pelletier |
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| Rok vydání: | 1983 |
| Předmět: | |
| Zdroj: | Journal of Symbolic Logic. 48:475-481 |
| ISSN: | 1943-5886 0022-4812 |
| Popis: | T.K. Menas [4, pp. 225-234] introduced a combinatorial property X(,u) of a measure u1 on a supercompact cardinal /c and proved that measures with this property also have the partition property. We prove here that Menas' property is not equivalent to the partition property. We also show that if a is the least cardinal greater than / such that Pa bears a measure without the partition property, then a is inaccessible and II,indescribable. This paper includes (in ?3) detailed proofs of some theorems of the first author that were initially sketched in an unpublished handwritten manuscript, [2], distributed in 1971. The impetus for publication of these results at this time arises from a theorem of the second author (Theorem 1, below) that makes use of these earlier results. To distinguish the theorems that are stated and proved in the present paper from those that are cited from the literature, the former will be numbered whereas the latter will be lettered. ?0 includes a brief history and motivation of the concepts studied in this paper. ?1 contains the basic definitions and summarizes some results from the litera |
| Databáze: | OpenAIRE |
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