## Abstract We show that it is consistent, relative to a supercompact limit of supercompact cardinals, for the least strongly compact cardinal k to be both the least measurable cardinal and to be > 2^k^ supercompact.
On the least strongly compact cardinal
โ Scribed by Arthur W. Apter
- Book ID
- 112885673
- Publisher
- The Hebrew University Magnes Press
- Year
- 1980
- Tongue
- English
- Weight
- 457 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0021-2172
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๐ SIMILAR VOLUMES
ON COMPACT CARDINALS by J. L. BELL in London (Great Britain) Let x be a cardinal and L a language. x is said to be L-compact if whenever ,Z is a set of sentences of L such that any subset of L' of power < x has a model, so does Z. If 9 is a class of languages, we say that x is 9-compact if x is L-co
It is proved that ff strongly compact cardinals ale consistent, then it is consistent that the fb~t such cardinal is the first measurable. On the othat hand, if it is consistent to asmlne the existence of supcrcompact cardinal, then it is consistent to assume that it is the t~trst strongly compact c