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Bulletin of the American Mathematical Society
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Cardinal arithmetic for skeptics

Author(s): Saharon Shelah
Journal: Bull. Amer. Math. Soc. 26 (1992), 197-210.
MSC (2000): Primary 03E05; Secondary 03E10, 03E35, 04A10, 06E05, 08A05, 20A15, 54A25
MathSciNet review: 1112424
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References:

[ARSh 153]
U. Abraham, M. Rubin, and S. Shelah, On the consistency of some partition theorems for continuous colorings and the structure of $ {\aleph _1}$-dense real order types, Ann. Pure Appl. Logic 29 (1985), 123-206. MR 801036 (87d:03132)

[B]
J. Baumgartner, Almost disjoint sets, the dense set problem, and the partition calculus, Ann. Pure Appl. Logic 9 (1975), 401-439. MR 0401472 (53:5299)

[BP]
J. Baumgartner and K. Prikry, On a theorem of Silver, Discrete Math. 14 (1976), 17-22. MR 0387061 (52:7908)

[BoSh 210]
R. Bonnet and S. Shelah, Narrow boolean algebras, Ann. Pure Appl. Logic 28 (1985), 1-12. MR 776283 (86g:06024)

[C]
P. Cohen, Set theory and the continuum hypothesis, Benjamin, NY, 1966. MR 0232676 (38:999)

[Cu]
J. Cummings, Consistency results in cardinal arithmetic, Ph. D. thesis, Cal-Tech, Pasadena, CA.

[CW]
J. Cummings and H. Woodin, preprint.

[DeJ]
K. Devlin and R. B. Jensen, Marginalia to a theorem of Silver, Proceedings of the Logic Colloquium, Kiel 1974 (G. H. Müller, A. Oberschelp, and K. Potthoff, eds.), Lecture Notes in Math., vol. 499, Springer-Verlag, Berlin, 1975, pp. 115-142. MR 0480036 (58:235)

[DoJ]
A. Dodd and R. B. Jensen, The core model, Annals Math. Logic (Ann. Pure Appl. Logic) 20 (1981), 43-75. MR 611394 (82i:03063)

[FW]
M. Foreman and H. Woodin, G.C.H can fail everywhere, Ann. of Math. (2) 133 (1991), 1-35. MR 1087344 (91k:03130)

[GH]
F. Galvin and A. Hajnal, Inequalities for cardinal powers, Ann. of Math. (2) 101 (1975), 491-498. MR 0376359 (51:12535)

[GHS]
J. Gertlis, A. Hajnal, and Z. Szentmiklossy, On the cardinality of certain Hausdorff spaces, Frolic Memorial Volume, accepted.

[Gi]
M. Gitik, The negation of SCH from $ o{(\kappa )^{ + + }}$, Ann. Pure Appl. Logic 43 (1989), 209-234. MR 1007865 (90h:03037)

[Gi1]
-, The strength of the failure of the singular cardinal hypothesis, preprint.

[GM]
M. Gitik and M. Magidor, The singular cardinal hypothesis revisited (in preparation).

[GiSh 344]
M. Gitik and S. Shelah, On certain indestructibility of stray cardinals and a question of Hajnal, Arch. Math Logic 28 (1989), 35-42. MR 987765 (90e:03063)

[GiSh 412]
M. Gitik and S. Shelah, More on ideals with simple forcing notions, Ann. Pure Appl. Logic (to appear). MR 1213273 (94c:03070)

[JP]
T. Jech and K. Prikry, Ideals over uncountable sets: applications of almost disjoint sets and generic ultrapowers, Mem. Amer. Math. Soc. 214 (1979). MR 519927 (80f:03059)

[JeSh 385]
T. Jech and S. Shelah, On a conjecture of Tarski on products of cardinals, Proc. Amer. Math. Soc. 112 (1991), 1117-1124. MR 1070525 (91j:03066)

[Mg]
M. Magidor, On the singular cardinals problem I, Israel J. Math. 28 (1977), 1-31. MR 0491183 (58:10449a)

[Mg1]
-, On the singular cardinals problem II, Ann. of Math. (2) 106 (1977), 517-547. MR 0491184 (58:10449b)

[Mg2]
-, Chang's conjecture and powers of singular cardinals, J. Symbolic Logic 42 (1977), 272-276. MR 0485375 (58:5221)

[M]
W. Mitchell, The core model for sequences of measures I, Math. Proc. Cambridge Philos. Soc. 95 (1984), 229-260. MR 735366 (85i:03163)

[Pr]
K. Prikry, Changing measurable to accessible cardinals, Rozprawy Mat. LXVIII (1970), 1-52.

[Sh 68]
S. Shelah, Joñsson algebras in successor cardinals, Israel J. Math. 39 (1978), 475-480. MR 0505434 (58:21572)

[Sh 71]
-, A note on cardinal exponentiation, J. Symbolic Logic 45 (1980), 56-66. MR 560225 (82c:03070)

[Sh 111]
-, On powers of singular cardinals, Notre Dame J. Formal Logic 27 (1986), 263-299. MR 842153 (87j:04006)

[Sh b]
-, Proper Forcing, Lecture Notes in Math., vol. 940, Springer-Verlag, Berlin, 1982. MR 675955 (84h:03002)

[Sh 137]
-, The singular cardinal problem: independence results, Proceedings of a Symposium on Set Theory, Cambridge 1978 (A. Mathias, ed.), London Math Soc. Lecture Notes Ser., vol. 87, Cambridge Univ. Press, Cambridge and New York, 1983, pp. 116-134. MR 823777 (87b:03114)

[Sh 161]
-, Incompleteness in regular cardinals, Notre Dame J. Formal Logic 26 (1985), 195-228. MR 796637 (87f:03095)

[Sh 256]
-, More on powers of singular cardinals, Israel J. Math. 59 (1987), 263-299. MR 920498 (89h:03082)

[Sh 280]
-, Strong negative partition relations above the continuum, J. Symbolic Logic 55 (1990), 21-31. MR 1043541 (91b:03083)

[Sh 282]
-, Successors of singulars, productivity of chain conditions, and cofinalities of reduced products of cardinals, Israel J. Math. 60 (1987), 146-166.

[Sh 327]
-, Strong negative partition relations below the continuum, Acta Math. Hungar. in press.

[Sh 410]
-, More on cardinal arithmetic, Arch. Math. Logic (to appear). MR 1245523 (94j:03100)

[Sh 413]
-, More Jonsson algebras and coloring, preprint.

[Sh 420]
-, Advances in cardinal arithmetic, to appear.

[Sh 430]
-, Further cardinal arithmetic, preprint.

[Sh-g]
-, Cardinal arithmetic, OUP, (to appear).

[ShW 159]
S. Shelah and H. Woodin, Forcing the failure of the CH, J. Symbolic Logic 49 (1984), 1185-1189. MR 771786 (86h:03087)

[Sc]
D. Scott, Measurable cardinals and constructible sets, Bull. Acad. Pol. Sci. Ser. Math. Astron. Phys. 9 (1961), 521-524. MR 0143710 (26:1263)

[Si]
J. Silver, On the singular cardinal problem, Proceedings ICM, Vancouver 1974, vol. I, pp. 265-268, MR 0429564 (55:2576)

[So]
R. Solovay, Strongly compact cardinals and the GCH, Proceedings of the Tarski Symposium, Berkeley 1971, Proc. Sympos. Pure Math., vol. xxi, Amer. Math. Soc., Providence, RI, 1974, pp. 365-372. MR 0379200 (52:106)

[T]
S. Todorčevic, Remarks on chain conditions in products, Compositio Math. 56 (1985), 295-302. MR 799818 (87b:04003)

[T1]
-, Remarks on cellularity in products, Compositio Math. 57 (1986), 357-372. MR 829326 (88h:54009)

[W]
H. Woodin, The Collected Unwritten Works of H. Woodin.

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Additional Information:

DOI: 10.1090/S0273-0979-1992-00261-6
PII: S 0273-0979(1992)00261-6
Copyright of article: Copyright 1992, American Mathematical Society




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