共查询到20条相似文献,搜索用时 15 毫秒
1.
David Chodounský Osvaldo Guzmán González Michael Hrušák 《Archive for Mathematical Logic》2016,55(3-4):493-504
We study the Mathias–Prikry and the Laver type forcings associated with filters and coideals. We isolate a crucial combinatorial property of Mathias reals, and prove that Mathias–Prikry forcings with summable ideals are all mutually bi-embeddable. We show that Mathias forcing associated with the complement of an analytic ideal always adds a dominating real. We also characterize filters for which the associated Mathias–Prikry forcing does not add eventually different reals, and show that they are countably generated provided they are Borel. We give a characterization of \({\omega}\)-hitting and \({\omega}\)-splitting families which retain their property in the extension by a Laver type forcing associated with a coideal. 相似文献
2.
Jacques Stern 《Israel Journal of Mathematics》1975,20(2):97-110
Assuming projective determinacy when it is needed, we prove some structure theorems in the measure theory and the category theory of the analytical hierarchy. 相似文献
3.
Justin Tatch Moore 《Acta Mathematica》2013,210(1):173-183
The purpose of this article is to prove that the forcing axiom for completely proper forcings is inconsistent with the continuum hypothesis. This answers a longstanding problem of Shelah. 相似文献
4.
We show a general scheme of Ramsey-type results for partitions of countable sets of finite functions, where “one piece is big” is interpreted in the language originating in creature forcing. The heart of our proofs follows Glazer’s proof of the Hindman Theorem, so we prove the existence of idempotent ultrafilters with respect to suitable operation. Then we deduce partition theorems related to creature forcings. 相似文献
5.
David Asperó Sy-David Friedman Miguel Angel Mota Marcin Sabok 《Annals of Pure and Applied Logic》2013
We study the spectrum of forcing notions between the iterations of σ-closed followed by ccc forcings and the proper forcings. This includes the hierarchy of α-proper forcings for indecomposable countable ordinals α, the Axiom A forcings and forcings completely embeddable into an iteration of a σ-closed followed by a ccc forcing. For the latter class, we present an equivalent characterization in terms of Baumgartner?s Axiom A. This resolves a conjecture of Baumgartner from the 1980s. 相似文献
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We study the Mathias–Prikry and Laver–Prikry forcings associated with filters on ω. We give a combinatorial characterization of Martin?s number for these forcing notions and present a general scheme for analyzing preservation properties for them. In particular, we give a combinatorial characterization of those filters for which the Mathias–Prikry forcing does not add a dominating real. 相似文献
9.
We define a global order of norms using strongly optimal strategies in Blackwell games and prove that it is a prewellordering
under the assumption of the Axiom of Blackwell determinacy. 相似文献
10.
Giorgio Laguzzi 《Archive for Mathematical Logic》2014,53(5-6):487-502
In this paper we analyse some notions of amoeba for tree forcings. In particular we introduce an amoeba-Silver and prove that it satisfies quasi pure decision but not pure decision. Further we define an amoeba-Sacks and prove that it satisfies the Laver property. We also show some application to regularity properties. We finally present a generalized version of amoeba and discuss some interesting associated questions. 相似文献
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12.
N. T. Kogabaev 《Siberian Mathematical Journal》2013,54(2):247-255
We study computable representations of projective planes and prove that the class of all pappian projective planes and the class of all desarguesian projective planes have no computable numberings (up to computable isomorphism). 相似文献
13.
We study automatic presentations of projective planes and prove that no freely generated projective plane has any automatic presentations. Every desarguesian (pappian) projective plane is shown to be automatically presentable if and only if it is finite. 相似文献
14.
Alexander Kuznetsov 《Publications Mathématiques de L'IHéS》2007,105(1):157-220
We introduce a notion of homological projective duality for smooth algebraic varieties in dual projective spaces, a homological
extension of the classical projective duality. If algebraic varieties X and Y in dual projective spaces are homologically
projectively dual, then we prove that the orthogonal linear sections of X and Y admit semiorthogonal decompositions with an
equivalent nontrivial component. In particular, it follows that triangulated categories of singularities of these sections
are equivalent. We also investigate homological projective duality for projectivizations of vector bundles. 相似文献
15.
A subset of projective space is called convex if its intersection with every line is connected. The complement of a projective convex set is again convex. We prove that for any projective convex set there exists a pair of complementary projective subspaces, one contained in the convex set and the other in its complement. This yields their classification up to homotopy. 相似文献
16.
We prove that the Sacks forcing collapses the continuum onto , answering the question of Carlson and Laver. Next we prove that if a proper forcing of the size at most continuum collapses
then it forces .
Received July 4, 1994 相似文献
17.
Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic
to
. We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional regular planes
are lines, prove that homeomorphisms preserving plane curves are smooth collineations, and prove a variety of results analogous
to the theory of classical projective planes.
*Thanks to Robert Bryant and John Franks. 相似文献
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19.
Saharon Shelah 《Israel Journal of Mathematics》1994,88(1-3):159-174
We prove that any Souslin c.c.c. forcing notion which adds a nondominated real adds a Cohen real. We also prove that any Souslin c.c.c. forcing adds a real which is not on any old “narrow” tree. 相似文献
20.
M. É. Kazaryan 《Journal of Mathematical Sciences》1990,52(4):3338-3349
The paper studies the bifurcations of the flat points of projective curves and describes the singularities of the boundaries of the regions where typical three-parameter families of curves have no flat points. A flat-point-preserving transformation group of projective curves is introduced. Finite determinacy and versality theorems are proved for this group. A duality theorem is proved and some results concerning the connection of this problem with other problems of singularity theory are presented.Translated from Itogi Nauki i Tekhniki, Seriya Sovermennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 33, pp. 215–232, 1988. 相似文献