共查询到20条相似文献,搜索用时 328 毫秒
1.
Saharon Shelah 《Israel Journal of Mathematics》1981,40(1):1-32
We weaken the notion of proper to semi-proper, so that the important properties (e.g., being preserved by some interations)
are preserved, and it includes some forcing which changes the confinality of a regular cardinal >ℵ1 to ℵ0. So, using the right iteractions, we can iterate such forcing without collapsing ℵ1. As a result, we solve the following problems of Friedman, Magidor and Avraham, by proving (modulo large cardinals) the consistency
of the following with G.C.H.: (1) for everyS ⊑ ℵ2,S or ℵ2-S contains a closed copy of ω1 (2) there is a normal precipitous filterD on
(3) for every
is regular inL (δ ∩A)} is statonary. The results can be improved to equi-consistency; this will be discussed in a future paper.
The author thanks the United States-Israel Binational Science Foundation for supporting the research by grant 1110. 相似文献
2.
Let b denote the unboundedness number of ωω. That is, b is the smallest cardinality of a subset
such that for everyg∈ωω there isf ∈ F such that {n: g(n) ≤ f(n)}is infinite. A Boolean algebraB is wellgenerated, if it has a well-founded sublatticeL such thatL generatesB. We show that it is consistent with ZFC that
, and there is a Boolean algebraB such thatB is not well-generated, andB is superatomic with cardinal sequence 〈ℵ0, ℵ1, ℵ1, 1〉. This result is motivated by the fact that if the cardinal sequence of a Boolean algebraB is 〈ℵ0, ℵ0, λ, 1〉, andB is not well-generated, then λ≥b. 相似文献
3.
Dale Alspach 《Israel Journal of Mathematics》2000,117(1):239-259
It is shown that a
-space with separable dual constructed by Bourgain and Delbaen has small Szlenk index and thus does not have a quotient isomorphic
toC(ωω). It follows that this is a
-space which is the same size asc
0 in the sense of the Szlenk index but does not containc
0. This has some consequences in the theory of uniform homeomorphism of Banach spaces. 相似文献
4.
For an idealJ on an infinite setX with add(J)=κ, let
be the smallest size of any subfamilyY ofJ with the property that any member ofJ can be covered by less than κ members ofY. We study the value of
forA in
, where
denotes the smallest [δ]<θ ideal onP
κ(λ). We also discuss the problem of whether there exists a setA such that
, or even
.
Some of the material in this paper originally appeared as part of the author's doctoral dissertation completed at the Université
de Caen, 1998.
Partially supported by the Israel Science Foundation. Publication 813. 相似文献
5.
We present S. Shelah’s result thatS
1
2
={δ<ω
2: cf(δ)=ω
1} may have the uniformization property (cf., §1, or [3] for a definition) for “well-chosen sequences”, 〈η
δ:δ∈S
1
2
^η
δ an increasingω
1-sequence of ordinals converging to δ〉. This implies that
, which shows that Gregory’ result (cf., [2]),
, is the best possible. 相似文献
6.
Saharon Shelah 《Israel Journal of Mathematics》1988,62(3):355-380
Aroused by Todorcevic’s breakthrough we prove here some complementary consistency results, mainly
. We also get some generalization of his theorem to, e.g.,λ↛
forλ regular notω-Mahlo.
The author thanks the NSF and N.S.E.R.C. for partially supporting the research. Preliminary versions of §3 and §2 were circulated
in November ’84 and February ’85, respectively. 相似文献
7.
Volker Turau 《Israel Journal of Mathematics》1988,62(2):206-212
For a finite groupG and some prime powerp
n
, the
-subgroup
is defined by
. Meixner proved that ifG is a finite solvable group and
for somen≧1, then the Fitting length of
is bounded by 4n. In the following note it is shown that the 2-length of
is at mostn. This result cannot be derived from Meixner’s paper, since his result implies only that the 2-length is bounded by 2n. 相似文献
8.
C. Bose 《Israel Journal of Mathematics》1993,83(1-2):129-152
A process (T, P) is said to have the “
” property if there is a uniform, positive lowerbound δ on the
separation between theT-P names of (almost) every pair of pointsx≠y. A finite group rotation with partition into distinct points provides a trivial example. Given any process having the
property we show that there exists a Bernoulli shiftB so thatT×B is measurably isomorphic to the natural extension of a piecewise monotone, continuous, and expanding map of the unit interval.
This construction is applied to produce interval maps which are ergodic but not weak-mixing, weak-mixing but not mixing, and
mixing but not exact with respect to their unique absolutely continuous invariant measures, in contrast with the results known
for piecewiseC
1+∈ expansive interval maps. In obtaining these examples we identify a number of nontrivial classes of automorphismsT which admit processes having the
property.
Supported by NSERC grant OGP0046586 90. 相似文献
9.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
10.
Götz Brunner 《Israel Journal of Mathematics》1972,12(3):306-313
In the definition ofCW-complexes, the one-point spaceP, respectively the spaceP∪* with basepoint *, play the roll of the only “building-stone”. Let
be a family of compact spaces. Then the definition of a generalizedCW-complex over
is obtained from the definition of aCW-complex by replacingP by the spaces of
and formation of the mapping cone by a slightly modified construction. LetCW
* denote the category of all pointed spaces which have the homotopy type of a generalizedCW-complex over
. If
, thenCW
* is the category of all pointedCW-spaces.CW
* is closed under the formation of direct sums and of mapping cones, cylinders and tori, and is formally characterized as
the smallest such subcategory of Top * containing the spaces W∪*,
. Following the methods of E. H. Brown, it is proved, that any half exact homotopy functor onCW
* is representable, and any cohomology theory onCW
is naturally equivalent to the cohomology theory of an Ω-spectrum; for example, the singular cohomo logy is representable
onCW
for any family
of compact spaces.
相似文献
11.
V. M. Petrogradsky 《Israel Journal of Mathematics》1999,113(1):323-339
Suppose that
% MathType!End!2!1! is a variety of Lie algebras, and letc
n(
% MathType!End!2!1!) be the dimension of the linear span of all multilinear words onn distinct letters in the free algebraF(
% MathType!End!2!1!,X) of the variety
% MathType!End!2!1!. We consider an exponential generating function
% MathType!End!2!1!, called the complexity function. The complexity function is an entire function of a complex variable provided
the variety of Lie algebras is nontrivial. In this paper we introduce the notion of complexity for Lie varieties in terms
of the growth of complexity functions; also we describe what the complexity means for the codimension growth of the variety.
Our main goal is to specify the complexity of a product of two Lie varieties in terms of the complexities of multiplicands.
The main observation here is thatC(
% MathType!End!2!1!),z) behaves like a composition of three functionsC(
% MathType!End!2!1!),z), exp(z), andC(
% MathType!End!2!1!),z).
Partially supported by grant RFFI 96-01-00146; the author is grateful to the University of Bielefeld for hospitality, where
he was DAAD-fellow. 相似文献
12.
Saharon Shelah 《Israel Journal of Mathematics》1977,28(3):193-204
We prove the consistency with ZFC+G.C.H. of an assertion, which implies several consequences of
, which
implies their negation.
The author would like to thank the United States-Israel Binational Science Foundation for partially supporting this research
by grant 1110. 相似文献
13.
We examine the existence of universal elements in classes of infinite abelian groups. The main method is using group invariants
which are defined relative to club guessing sequences. We prove, for example:Theorem:For n≧2, there is a purely universal separable p-group in ℵ
n
if, and only if,
.
Partially supported by the United States-Israel Binational Science Foundation. Publication number 455. 相似文献
14.
Given ∈, we construct a sequence
, … of Borel sub-sigma-algebras on the unit interval with the following property. Suppose the identity functionf(x)=x is transformed by successive conditioning on
, then
, then
, Then the lim sup, with respect ton, will exceed (pointwise almost-everywhere) 1−∈ and its lim inf will be less than ∈.
The sequence of functions also will fail to converge in the
. This contrasts with the long-open conjecture that if all the
come from a finite set of sigma-algebras, then the resulting sequence of functions must converge in
.
J. L. King was partially supported by NSF grant DMS-9112595. 相似文献
15.
We prove that if is the error of a simple quadrature formula and ω(ε, δ)1 is the integral modulus of continuity, then, for any δ ≥/π andn,r = 1, 2, …, the following equality is true: whereD
r
is the Bernoulli kernel. 相似文献
16.
Let II be a bounded symmetric domain, ω ⇉ I a bounded subdomain, and let
denote the weighted Bergman space of holomorphic square integrable functions on I. Let Tλ, ω be the Berezin-Toeplitz operator on
with symbol χΩ and kth eigenvalue λ
k
(T
λ,Ω). We prove that for δ1 sufficiently close to 0 and δ2 sufficiently close to 1 the estimate
holds for all domains ω satisfying the condition |{z ∈ I |d(z, Ω) < ε}| ≤c|Ω|, where d is the invariant distance on I and |ω| is the invariant volume of ω. The proof is based on the fact that the
operator norm of the Berezin transform is smaller than 1. Our main technical tool are some of the formulae for the Berezin
transform obtained by Unterberger and Upmeier in [11]. 相似文献
17.
M. Zippin 《Israel Journal of Mathematics》1966,4(3):199-204
A basis
is constructed inc
0 such that there exists no bounded linear projection ofc
0 onto the subspace spanned by a certain subsequence
of
.
This is part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem under the suppervision of Professor
A. Dvoretzky and Dr. J. Lindenstrauss. The author wishes to thank Dr. Lindenstrauss for his helpful advice. 相似文献
18.
LetF be a commutative ring with 1, letA, be a primeF-algebra with Martindale extended centroidC and with central closureA
c
and letR be a noncentral Lie ideal of the algebraA generatingA. Further, letZ(R) be the center ofR, let
be the factor Lie algebra and let δ:
be a Lie derivation. Suppose that char(A) ≠ 2 andA does not satisfySt
14, the standard identity of degree 14. We show thatR ΩC =Z(R) and there exists a derivation of algebrasD:A →A
c
such that
for allx∈R. Our result solves an old problem of Herstein. 相似文献
19.
In this paper we prove two (rather unrelated) theorems about projective sets. The first one asserts that subsets of ℵ1 which are
in the codes are constructible; thus it extends the familiar theorem of Shoenfield that
subsets of ω are constructible. The second is concerned with largest countable
sets and establishes their existence under the hypothesis of Projective Determinacy and the assumption that there exist only
countably many ordinal definable reals.
Y. N. Moschovakis is a Sloan Foundation Fellow. During the preparation of this paper, both authors were partially supported
by NSF Grant GP-27964. 相似文献
20.
M. Rudelson 《Israel Journal of Mathematics》1999,111(1):143-155
Lett≥1 and letn, M be natural numbers,n<M. Leta=(a
i,j
) be ann xM matrix whose rows are orthonormal. Suppose that the ℓ2-norms of the columns ofA are uniformly bounded. Namely, for allj
Using majorizing measure estimates we prove that for every ε>0 there exists, a setI ⊃ {1,…,M} of cardinality at most
such that the matrix
, whereA
I
=(a
i,j
)
j∈I
, acts as a (1+ε)-isomorphism from ℓ
2
n
into
.
Research supported in part by a grant of the US-Israel BSF. Part of this research was performed when the author held a postdoctoral
position at MSRI. Research at MSRI was supported in part by NSF grant DMS-9022140. 相似文献