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Some principles related to Chang's conjecture

Hans-Dieter Donder, Jean-Pierre Levinski
1989 Annals of Pure and Applied Logic  
We determine the consistency strength of the negation of the transversal hypothesis. We also study other variants of Chang's conjecture. The transversal hypothesis TH is the statement that there exist o2 many almost disjoint functions from o1 to o. This seems tc be a basic principle because it impiies the negation of Chang's conjecture, that no wl-complete uniform filter on o1 is wrsaturated and that every uniform ultrafilter on o1 is regular. The main aim of this paper is to determine the
more » ... stency strength of the negation of 'PH. This will be done in Section 7 where we shcw that ZFC + 1 is equiconsistent to ZFC + "there exists a ( J/J denotes that consistencywise ZFC + @ is n the other hand, # = pv denotes that ZFC + 9 ally, dealing with games we often abbreviate 'winning strategy' by 'w.s.'. ng 3 conjecture If K = oI, Chang's conjecture is just K3m2, we can ac tually consider various versions. very structure % = (K+, (&o) of countable type, there easily seen to be equivalent. Concerning the third, shall Some principles reilated to Char@ conjecture 41
doi:10.1016/0168-0072(89)90030-4 fatcat:fbg64255vbaqnea6uwccbq7gqq

Some stationary subsets of $\mathcal{P}(\lambda)$

Hans-Dieter Donder, Peter Koepke, Jean-Pierre Levinski
1988 Proceedings of the American Mathematical Society  
Let k, and A be uncountable cardinals such that k < X, and set S(k, X) = {X € PkW\ \XHk\ < \X\}. We determine the consistency strength of the statement "(3A > k)(S(k, X) is stationary in PK(X))" using a new type of partition cardinals. In addition, we show that the property "S{k, k+) is stationary in Pk(k.+ )" is much stronger. Let k and A be two cardinals such that k is regular and A > k > uj. Set S(k, A) = {X G PK{X)\ \X n k| < \X\}. Baumgartner and Baldwin introduced this set (see [2] ) and
more » ... btained partial results concerning the question whether S(k,X) is stationary in PK(X). In this paper we strengthen their results. We determine the exact consistency strength of the property "(3A > k)(S(k, A) is stationary in PK(X))V. Moreover, we show that this property becomes much stronger if we also require that the gap between k and A is small. Recall that if k is /c+-supercompact, then S(k,k+) is stationary in Pk(k+) (see [1] ).
doi:10.1090/s0002-9939-1988-0934882-6 fatcat:fmtx4wrjsjghdbrhvhatlehft4

Page 16 of BGR. Business and Government Review Vol. 5, Issue 3 [page]

1964 BGR. Business and Government Review  
Rise of David Levinsky, 1917 Collins, Norman Gold for my Bride, 1940 Rise and fall of an English businessman.  ...  Block, Jean R. — y Co., 1929 The sacrifice of ideals accompanying the ma¬ terial success of a Jewish family of weavers in France.  ... 

Page 2428 of Mathematical Reviews Vol. , Issue 89D [page]

1989 Mathematical Reviews  
, Jean-Pierre Levitz, Hilbert Levy, Mireille BO TERE, cccccccccee See Levi, Roni N.  ...  Le Boudec, Jean-Yves OE 58061 ID 5 sicceenainicietiiiendalaad 92003 L’Ecuyer, Pierre Lee, Lee, Lee, Lee, Lee, Lee, Lee, Lee, Lee, Sang Jeong ...  ... 

Page 5410 of Mathematical Reviews Vol. , Issue 86k [page]

1986 Mathematical Reviews  
Lecoutre, Jean-Pierre Le Doussal, Pierre Ledoux, Michel Lé Ding Trang Lee, Chia-Hoang Lee, Clarence E. ...... Lee, H. ...  ...  Le Van Hot Levant, Leonid See *00001lab Lévardi, Ladszlé Levcopoulos, Christos R.D Levinski, Levinskil, S. V. ....... Levitt, Norman Levy, Haim Levy, Lawrence S. .... Lewis, J.  ... 

Page 6159 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
............0.000. 68024 Leung, Man Chun Leung, Pui Fai Leutwiler, Heinz Le Van Hoang I Ga OM. cs ce vccatsaccisasaces 82090 i i 35008,58154 BN IIE onde sasecdcnocxditaanecatenn 81280 Levine, Herbert Levinski  ...  Lingas, Andrzej po) ee See Linhart, Johann Linhart, Johann WO tS hac hivensersnccaiedse 51016 Linz, Peter Fy We daerakckig dncn Gace rcatescceec 62086 Ligme, Ferkescccscsces 35026, See also * 00014 Lions, Pierre-Louis  ... 

Page 8158 of Mathematical Reviews Vol. , Issue 99k [page]

1999 Mathematical Reviews  
CRAIN SSO TR. oi ceca vcsacciacs 53078 Lechtenfeld, Olaf 81300-81301 Lecomte, Alain Lecomte, Pierre B. A.  ...  David Levikson, Benny Ue ae Levine; FIGWAIG A... csc cca snaes 35124 Levinski, Vladimir See Levinskii, V. B.  ... 

Page 4831 of Psychological Abstracts Vol. 81, Issue 10 [page]

1994 Psychological Abstracts  
Michael, 37858 Malone, Jean, 37685 Malott, Richard W., 39191 Malotte, C.  ...  ., 36270 Lefcourt, Ilene Sackler, 37036 Lefebvre, Pierre J., 38698 Lefebvre, Louis, 36141 LeFevre, Jo-Anne, Pong , Gordon E.. 35971 le range, Daniel, 37876, 38348 Lehman, A.  ... 

Page 636 of Mathematical Reviews Vol. , Issue 91B [page]

1991 Mathematical Reviews  
Lévy (IL-HEBR) 91b:03087 03E35 03505 Donder, Hans-Dieter (D-FUB-2); Levinski, Jean-Pierre (1-DTM) Some principles related to Chang’s conjecture. Ann. Pure Appl. Logic 45 (1989), no. 1, 39-101.  ...  Pierre Matet (F-CAEN) 91b:03089 03E40 Wehrung, Friedrich (1-OHS) Nonabsoluteness of elementary embeddings. J. Symbolic Logic 54 (1989), no. 3, 774-778.  ... 

Page 386 of Mathematical Reviews Vol. 25, Issue 2 [page]

1963 Mathematical Reviews  
.-+++-- 1916 Kahane, Jean-Pierre ...... 1291 Kaliski, Sylwester ........ 1715 ti, go tad 6s «be b04 1701 Kanno, Teuneo........... 1243 Kantorovié, L.  ...  I. .... 1964, 1967 Deis Mivescccesceseegs 1245 Levinsky, Ely 8........... 1795 CTL Mon cccss gp shane 1152 Lianis, George .........-- 716 Linnik, Ju. V. ..... 1097b, 1572 Littlewood, J.  ... 

Page 510 of Mathematical Reviews Vol. , Issue 96a [page]

1996 Mathematical Reviews  
of this criterion is supported by our experimental results.” 96a:76042 76E15 76E30 76RO0S5 Aniss, Said (F-NANC-LM; Vandoeuvre-les-Nancy) ; Souhar, Mohamed (F-NANC-LM; Vandoeuvre-les-Nancy) ; Brancher, Jean-Pierre  ...  See also 35020, 35069, 35129, 35142, 35143, 35144, 35145, 35146, 35147, 35148, 35169, 65128, 70014. 76E Hydrodynamic stability 96a:76041 76E05 76C05 Levinski, Vladimir |Levinskii, V. B.]  ... 

Page 416 of National Union Catalog Vol. 7, Issue [page]

1958 National Union Catalog  
The rise of David Levinsky. New York, Ilarper ,1960, 21 cm. (Harper torehbooks, Introd. by John Higham. TB1028, The Academy Proll , 1. Title.  ...  (Series) MdBJ Cty NjR Cahen, Gilbert, 1904- Nuclear engineering, by Gilbert Cahen ,and, Pierre Treille. Translated by Gilbert B. Melese. Boston, Allyn and Bacon, 1961. Wag Pe Ae Trane atios Préc!  ... 

Page 3918 of Mathematical Reviews Vol. , Issue 96g [page]

1996 Mathematical Reviews  
, Jean-Pierre (F-CAEN; Caen) Filters and large cardinals.  ...  Summary: “For each prime p, a Fraenkel-Mostowski model is constructed in which there are two elementary abelian p-groups with the same cardinality that are not isomorphic.” 96g:03085 03E35 03E55 Levinski  ... 

Page 5794 of Mathematical Reviews Vol. , Issue 91K [page]

1991 Mathematical Reviews  
Bukovsky (CS-SFRK) 91k:03124 03E05 03E55 Carr, Donna M. (1-WIP); Levinski, Jean-Pierre (1-OH); Pelletier, Donald H. (3-YORK) On the existence of strongly normal ideals over P,./. Arch. Math.  ... 

Page 3550 of Mathematical Reviews Vol. , Issue 91G [page]

1991 Mathematical Reviews  
Bruno Poizat (Lyon) 91g:03071 03C52 03C55 03E40 Levinski, Jean-Pierre (1-DTM); Magidor, Menachem (IL-HEBR); Shelah, Saharon (IL-HEBR) Chang’s conjecture for ¥,,. Israel J.  ... 
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