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1.
Arthur W. Apter 《Archive for Mathematical Logic》2000,39(3):209-211
We give a new proof using iterated Prikry forcing of Magidor's theorem that it is consistent to assume that the least strongly
compact cardinal is the least supercompact cardinal.
Received: 8 December 1997 / Revised version: 12 November 1998 相似文献
2.
Paul Corazza 《Archive for Mathematical Logic》2000,39(3):219-226
The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended language , and that asserts the existence of a nontrivial elementary embedding . The well-known inconsistency proofs are avoided by omitting from the schema all instances of Replacement for j-formulas. We show that the theory ZFC + V = HOD + WA is consistent relative to the existence of an embedding. This answers a question about the existence of Laver sequences for regular classes of set embeddings: Assuming there is an -embedding, there is a transitive model of ZFC +WA + “there is a regular class of embeddings that admits no Laver sequence.”
Received: 7 July 1998 / Revised version: 5 November 1998 相似文献
3.
Wojciech Młtkowski 《Probability Theory and Related Fields》1999,115(4):579-596
We study noncommutative probability spaces endowed with infinite sequences of states. Following ideas of Cabanal-Duvillard we extend the notion of conditional freeness. Free product of such spaces is justified by constructing an appropriate ⋆-representation. Finally, we provide limit theorems and describe the sequences of orthogonal polynomials related to the limit measures. Received: 4 November 1998 / Revised version: 22 April 1999 相似文献
4.
Hideki Tanemura 《Probability Theory and Related Fields》1997,109(2):275-299
Summary. Dirichlet forms associated with systems of infinitely many Brownian balls in ℝ
d
are studied. Introducing a linear operator L
0 defined on a space of smooth local functions, we show the uniqueness of Dirichlet forms associated with self adjoint Markovian
extensions of L
0. We also discuss the ergodicity of the reversible process associated with the Dirichlet form.
Received: 18 July 1996/In revised form: 13 February 1997 相似文献
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Christian Bär 《Inventiones Mathematicae》1999,138(1):183-202
Consider a nontrivial smooth solution to a semilinear elliptic system of first order with smooth coefficients defined over
an n-dimensional manifold. Assume the operator has the strong unique continuation property. We show that the zero set of the solution
is contained in a countable union of smooth (n−2)-dimensional submanifolds. Hence it is countably (n−2)-rectifiable and its Hausdorff dimension is at most n−2. Moreover, it has locally finite (n−2)-dimensional Hausdorff measure. We show by example that every real number between 0 and n−2 actually occurs as the Hausdorff dimension (for a suitable choice of operator). We also derive results for scalar elliptic
equations of second order.
Oblatum 22-V-1998 & 26-III-1999 / Published online: 10 June 1999 相似文献
8.
Ralf-Dieter Schindler 《Archive for Mathematical Logic》1999,38(8):515-520
Suppose that there is no transitive model of ZFC + there is a strong cardinal, and let K denote the core model. It is shown that if has the tree property then and is weakly compact in K.
Received: 11 June 1997 相似文献
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We consider a class of degenerate elliptic operators on a torus and prove that global hypoellipticity is equivalent to an
algebraic condition involving Liouville vectors and simultaneous approximability. For another class of operators we show that
the zero order term may influence global hypoellipticity.
Received August 13, 1997 相似文献
11.
Continuing [6], [8] and [16], we study the consequences of the weak Freese-Nation property of (?(ω),⊆). Under this assumption,
we prove that most of the known cardinal invariants including all of those appearing in Cichoń's diagram take the same value
as in the corresponding Cohen model. Using this principle we could also strengthen two results of W. Just about cardinal sequences
of superatomic Boolean algebras in a Cohen model. These results show that the weak Freese-Nation property of (?(ω),⊆) captures
many of the features of Cohen models and hence may be considered as a principle axiomatizing a good portion of the combinatorics
available in Cohen models.
Received: 7 June 1999 / Revised version: 17 October 1999 /?Published online: 15 June 2001 相似文献
12.
Lucio Guerra 《manuscripta mathematica》1999,98(1):1-8
We provide a general estimate for the number of irreducible components of a Chow variety, the variety that parametrizes algebraic
cycles of given dimension and degree contained in a projective variety. The result is then applied to obtain an upper bound
for the finite number of surfaces of general type that are images of a fixed surface.
Received: 29 January 1998 / Revised version: 24 June 1998 相似文献
13.
Summary. Let be a complex polynomial of
degree with and Cauchy radius 1 about the
origin. We discuss the order of magnitude
of the minimal number such that
Previous estimates of are improved to . Some other related properties of these polynomials
are also exhibited.
Received March 3, 1993 相似文献
14.
Daisuke Matsushita 《Mathematische Annalen》2001,321(4):755-773
We classify singular fibres over general points of the discriminant locus of projective Lagrangian fibrations over 4-dimensional
holomorphic symplectic manifolds. The singular fibre F is the following either one: F is isomorphic to the product of an elliptic curve and a Kodaira singular fibre up to finite unramified covering or F is a normal crossing variety consisting of several copies of a minimal elliptic ruled surface of which the dual graph is
Dynkin diagram of type or . Moreover, we show all types of the above singular fibres actually occur.
Received: 10 March 2000 / Revised version: 29 September 2000 / Published online: 24 September 2001 相似文献
15.
Peter Vermeire 《Mathematische Zeitschrift》2002,242(1):75-95
We show how to use information about the equations defining secant varieties to smooth projective varieties in order to construct
a natural collection of birational transformations. These were first constructed as flips in the case of curves by M. Thaddeus
via Geometric Invariant Theory, and the first flip in the sequence was constructed by the author for varieties of arbitrary
dimension in an earlier paper. We expose the finer structure of a second flip; again for varieties of arbitrary dimension.
We also prove a result on the cubic generation of the secant variety and give some conjectures on the behavior of equations
defining the higher secant varieties.
Received: 29 November 1999; in final form: 4 September 2000 / Published online: 23 July 2001 相似文献
16.
(i) every 2-connected graph on n vertices can be made 4-connected by adding at most n new edges, and (ii) every 3-connected and 3-regular graph on n≥8 vertices can be made 4-connected by adding n/2 new edges. Received October 1995 / Revised version received March 1997 Published online March 16, 1999 相似文献
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Heike Mildenberger 《Archive for Mathematical Logic》2001,40(2):93-112
We show that the Filter Dichotomy Principle implies that there are exactly four classes of ideals in the set of increasing functions from the natural numbers. We thus answer two open questions on consequences of ? < ?. We show that ? < ? implies that ? = ?, and that Filter Dichotomy together with ? < ? implies ? < ?. The technical means is the investigation of groupwise dense sets, ideals, filters and ultrafilters. With related techniques we prove the new inequality ?≤ cf(?). Received: 9 October 1998 / Revised version: 18 August 1999 / Published online: 21 December 2000 相似文献
19.
Jörg Brendle 《Archive for Mathematical Logic》1998,37(3):183-197
We show the consistency of where is the size of the smallest off-branch family, and is as usual the dominating number. We also prove the consistency of with large continuum. Here, is the unbounding number, and is the almost disjointness number.
Received: September 12, 1996 / Revised version received: June 16, 1997 相似文献