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301.
We continue developing the general theory of forcing notions built with the use of norms on possibilities, this time concentrating on ccc forcing notions and classifying them.The first author thanks the Hebrew University of Jerusalem for its hospitality during his visits to Jerusalem. His research was also partially supported by a grant from the University Committee on Research of UNOThe research of the second author was partially supported by the Israel Science Foundation. Publication 672Mathematics Subject Classification (2000): Primary 03E35 Secondary; 03E40, 03E05Revised version: 30 September 2003 相似文献
302.
Let C be a finite connected graph for which there is a countable universal C-free graph, and whose tree of blocks is a path. Then the blocks of C are complete. This generalizes a result of Füredi and Komjáth, and fits naturally into a set of conjectures regarding the existence of countable C-free graphs, with C an arbitrary finite connected graph. 相似文献
303.
Saharon Shelah 《Archive for Mathematical Logic》2017,56(3-4):319-383
It is well known how to generalize the meagre ideal replacing \(\aleph _0\) by a (regular) cardinal \(\lambda > \aleph _0\) and requiring the ideal to be \(({<}\lambda )\)-complete. But can we generalize the null ideal? In terms of forcing, this means finding a forcing notion similar to the random real forcing, replacing \(\aleph _0\) by \(\lambda \). So naturally, to call it a generalization we require it to be \(({<}\lambda )\)-complete and \(\lambda ^+\)-c.c. and more. Of course, we would welcome additional properties generalizing the ones of the random real forcing. Returning to the ideal (instead of forcing) we may look at the Boolean Algebra of \(\lambda \)-Borel sets modulo the ideal. Common wisdom have said that there is no such thing because we have no parallel of Lebesgue integral, but here surprisingly first we get a positive \(=\) existence answer for a generalization of the null ideal for a “mild” large cardinal \(\lambda \)—a weakly compact one. Second, we try to show that this together with the meagre ideal (for \(\lambda \)) behaves as in the countable case. In particular, we consider the classical Cichoń diagram, which compares several cardinal characterizations of those ideals. We shall deal with other cardinals, and with more properties of related forcing notions in subsequent papers (Shelah in The null ideal for uncountable cardinals; Iterations adding no \(\lambda \)-Cohen; Random \(\lambda \)-reals for inaccessible continued; Creature iteration for inaccesibles. Preprint; Bounding forcing with chain conditions for uncountable cardinals) and Cohen and Shelah (On a parallel of random real forcing for inaccessible cardinals. arXiv:1603.08362 [math.LO]) and a joint work with Baumhauer and Goldstern. 相似文献
304.
We give a complete classification and construction of all normal subgroup lattices of 2-transitive automorphism groupsA(Ω) of linearly ordered sets (Ω, ≦). We also show that in each of these normal subgroup lattices, the partially ordered subset
of all those elements which are finitely generated as normal subgroups forms a lattice which is closed under even countably-infinite
intersections, and we derive several further group-theoretical consequences from our classification.
This research was supported by an award from the Minerva-Stiftung, München. The work was done during a stay of the first-named
author at The Hebrew University of Jerusalem in fall 1982. He would like to thank his colleagues in Jerusalem for their hospitality
and a wonderful time. 相似文献
305.
Assuming the consistency of ZFC we prove the claim in the title by showing the consistency with ZFC of: There exists a set
of realsA such that every function fromA toA is order preserving on an uncountable set. We prove related results among which is the consistency with ZFC of: Every function
from the reals into the reals is monotonic on an uncountable set.
I would like to thank the United States-Israel Binational Science Foundation for supporting this research by a grant. 相似文献
306.
We deal with the question of existence of a universal object in the category of universal locally finite groups; the answer
is negative for many uncountable cardinalities; for example, for 2ℵ
0, and assuming G.C.H. for every cardinal whose confinality is >ℵ0. However, if λ>κ when κ is strongly compact and of λ=ℵ0, then there exists a universal locally finite group of cardinality λ. The idea is to use the failure of the amalgamation
property in a strong sense. We shall also prove the failure of the amalgamation property for universal locally finite groups
by transferring the kind of failure of the amalgamation property from LF into ULF.
We would like to thank Simon Thomas for reading carefully a preliminary version of this paper, proving Lemma 20 and making
valuable remarks. Also we thank the United States—Israel Binational Science Foundation for partially supporting this work. 相似文献
307.
Saharon Shelah 《Journal of Combinatorial Theory, Series A》1974,16(2):199-208
A sufficient condition for the existence of a system of distinct representatives for a family S is that x?A?S implies the number of elements of A is not smaller than the number of sets in S to which x belongs. 相似文献
308.
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