Consistency results concerning supercompactness
Author:
Telis K. Menas
Journal:
Trans. Amer. Math. Soc. 223 (1976), 6191
MSC:
Primary 02K35; Secondary 02H13, 02K05
MathSciNet review:
0540771
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Abstract: A general framework for proving relative consistency results with regard to supercompactness is developed. Within this framework we prove the relative consistency of the assertion that every set is ordinal definable with the statement asserting the existence of a supercompact cardinal. We also generalize Easton's theorem; the new element in our result is that our forcing conditions preserve supercompactness.
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 W. B. Easton, Powers of regular cardinals, Ann. Math. Logic 1 (1970), 139178. MR 42 #4392. MR 0269497 (42:4392)
 [2]
 P. R. Halmos, Lectures on Boolean algebras, Van Nostrand Math. Studies, no. 1, Van Nostrand, Princeton, N.J., 1963. MR 29 #4713. MR 0167440 (29:4713)
 [3]
 T. J. Jech, Lectures in set theory, with particular emphasis on the method of forcing, Lecture Notes in Math., vol. 217, SpringerVerlag, Berlin and New York, 1971. MR 48 #105. MR 0321738 (48:105)
 [4]
 , Trees, J. Symbolic Logic 36 (1971), 114. MR 44 #1560. MR 0284331 (44:1560)
 [5]
 M. Magidor, Dissertation, University of Jerusalem, 1972.
 [6]
 J. R. Myhill and D. Scott, Ordinal definability, Proc. Sympos. Pure Math., vol. 13, part 1, Amer. Math. Soc., Providence, R.I., 1971, pp. 271278. MR 43 #7318. MR 0281603 (43:7318)
 [7]
 W. Reinhardt and R. Solovay, Strong axioms of infinity and elementary embeddings (to appear).
 [8]
 D. Scott and R. Solovay, Booleanvalued models for set theory, mimeographed notes.
 [9]
 J. R. Shoenfield, Unramified forcing, Proc. Sympos. Pure Math., vol. 13, part 1, Amer. Math. Soc., Providence, R.I., 1971, pp. 357381. MR 43 #6079. MR 0280359 (43:6079)
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 J. Silver, The independence of Kurepa's conjecture and twocardinal conjectures in model theory, Proc. Sympos. Pure Math., vol. 13, part 1, Amer. Math. Soc., Providence, R.I., 1971, pp. 383390. MR 43 #3112. MR 0277379 (43:3112)
 [11]
 , Forthcoming paper on large cardinals and the G.C.H.
 [12]
 R. M. Solovay and S. Tennenbaum, Iterated Cohen extensions and Souslin's problem, Ann. of Math. (2) 94 (1971), 201245. MR 45 #3212. MR 0294139 (45:3212)
 [13]
 D. H. Stewart, M. Sci. Thesis, Bristol, 1966.
 [14]
 F. Tall, Doctoral Dissertation, University of Wisconsin, 1969.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197605407718
PII:
S 00029947(1976)05407718
Keywords:
Large cardinals,
backward Easton forcing,
ordinal definability,
supercompactness
Article copyright:
© Copyright 1976
American Mathematical Society
