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On the first  strongly compact cardinals
Author:
Arthur W. Apter
Journal:
Proc. Amer. Math. Soc. 123 (1995), 2229-2235
MSC:
Primary 03E55; Secondary 03E35
MathSciNet review:
1249867
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Abstract: Using techniques of Kimchi and Magidor, we generalize an earlier result and show that it is relatively consistent for the first n strongly compact cardinals to be somewhat supercompact yet not fully supercompact.
- [A1]
Arthur
W. Apter, On the least strongly compact cardinal, Israel J.
Math. 35 (1980), no. 3, 225–233. MR 576474
(81h:03099), http://dx.doi.org/10.1007/BF02761194
- [A2]
Arthur
W. Apter, Some results on consecutive large cardinals, Ann.
Pure Appl. Logic 25 (1983), no. 1, 1–17. MR 722166
(85f:03053), http://dx.doi.org/10.1016/0168-0072(83)90051-9
- [KM]
Y. Kimchi and M. Magidor, The independence between the concepts of strong compactness and supercompactness (in preparation).
- [KP]
K.
Kunen and J.
B. Paris, Boolean extensions and measurable cardinals, Ann.
Math. Logic 2 (1970/1971), no. 4, 359–377. MR 0277381
(43 #3114)
- [L]
Richard
Laver, Making the supercompactness of 𝜅 indestructible
under 𝜅-directed closed forcing, Israel J. Math.
29 (1978), no. 4, 385–388. MR 0472529
(57 #12226)
- [LS]
A.
Lévy and R.
M. Solovay, Measurable cardinals and the continuum hypothesis,
Israel J. Math. 5 (1967), 234–248. MR 0224458
(37 #57)
- [Ma]
Menachem
Magidor, How large is the first strongly compact cardinal? or A
study on identity crises, Ann. Math. Logic 10 (1976),
no. 1, 33–57. MR 0429566
(55 #2578)
- [Me]
Telis
K. Menas, On strong compactness and supercompactness, Ann.
Math. Logic 7 (1974/75), 327–359. MR 0357121
(50 #9589)
- [SRK]
Robert
M. Solovay, William
N. Reinhardt, and Akihiro
Kanamori, Strong axioms of infinity and elementary embeddings,
Ann. Math. Logic 13 (1978), no. 1, 73–116. MR 482431
(80h:03072), http://dx.doi.org/10.1016/0003-4843(78)90031-1
- [A1]
- A. Apter, On the least strongly compact cardinal, Israel J. Math. 35 (1980), 225-233. MR 576474 (81h:03099)
- [A2]
- -, Some results on consecutive large cardinals, Ann. Pure Appl. Logic 25 (1983), 1-17. MR 722166 (85f:03053)
- [KM]
- Y. Kimchi and M. Magidor, The independence between the concepts of strong compactness and supercompactness (in preparation).
- [KP]
- K. Kunen and J. Paris, Boolean extensions and measurable cardinals, Ann. Math. Logic 2 (1971), 359-378. MR 0277381 (43:3114)
- [L]
- R. Laver, Making the supercompactness of
 indestructible under  -directed closed forcing, Israel J. Math. 29 (1978), 385-388. MR 0472529 (57:12226)
- [LS]
- A. Lévy and R. Solovay, Measurable cardinals and the continuum hypothesis, Israel J. Math. 5 (1967), 234-248. MR 0224458 (37:57)
- [Ma]
- M. Magidor, How large is the first strongly compact cardinal?, Ann. Math. Logic 10 (1976), 33-57. MR 0429566 (55:2578)
- [Me]
- T. Menas, On strong compactness and supercompactness, Ann. Math. Logic 7 (1975), 327-360. MR 0357121 (50:9589)
- [SRK]
- R. Solovay, W. Reinhardt, and A. Kanamori, Strong axioms of infinity and elementary embeddings, Ann. Math. Logic 13 (1978), 73-116. MR 482431 (80h:03072)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1995-1249867-6
PII:
S 0002-9939(1995)1249867-6
Article copyright:
© Copyright 1995 American Mathematical Society
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