共查询到20条相似文献,搜索用时 15 毫秒
1.
Teruyuki Yorioka 《Annals of Pure and Applied Logic》2010,161(4):469-487
We introduce a property of forcing notions, called the anti-, which comes from Aronszajn trees. This property canonically defines a new chain condition stronger than the countable chain condition, which is called the property .In this paper, we investigate the property . For example, we show that a forcing notion with the property does not add random reals. We prove that it is consistent that every forcing notion with the property has precaliber ℵ1 and for forcing notions with the property fails. This negatively answers a part of one of the classical problems about implications between fragments of . 相似文献
2.
Wang Wei 《Annals of Pure and Applied Logic》2010,161(10):1291-1298
It is shown that every locally countable upper semi-lattice of cardinality the continuum can be embedded into the Turing degrees, assuming Martin’s Axiom. 相似文献
3.
James E. Baumgartner 《Topology and its Applications》1985,19(3):211-225
Using side-by-side Sacks forcing, it is proved relatively consistent that the continuum is large and Martin's Axiom fails totally, that is, every c.c.c. space is the union of ?1 nowhere dense sets (equivelently, if P is a nontrivial partial ordering with the countable chain condition, then there are ?1 dense sets in P such that no filter in P meets them all). 相似文献
4.
Recently, the first two authors characterized in Di Nola and Dvure?enskij (2009) [1] subdirectly irreducible state-morphism MV-algebras. Unfortunately, the main theorem (Theorem 5.4(ii)) has a gap in the proof of Claim 10, as the example below shows. We now present a correct characterization and its correct proof. 相似文献
5.
Sy-David Friedman Radek Honzik Šárka Stejskalová 《Annals of Pure and Applied Logic》2018,169(6):548-564
Starting from a Laver-indestructible supercompact κ and a weakly compact λ above κ, we show there is a forcing extension where κ is a strong limit singular cardinal with cofinality ω, , and the tree property holds at . Next we generalize this result to an arbitrary cardinal μ such that and . This result provides more information about possible relationships between the tree property and the continuum function. 相似文献
6.
Athanassios Tzouvaras 《Annals of Pure and Applied Logic》2011,162(5):373
We prove a combinatorial result for models of the 4-fragment of the Simple Theory of Types (TST), TST4. The result says that if A=〈A0,A1,A2,A3〉 is a standard transitive and rich model of TST4, then A satisfies the 〈0,0,n〉-property, for all n≥2. This property has arisen in the context of the consistency problem of the theory New Foundations (NF). The result is a weak form of the combinatorial condition (existence of ω-extendible coherent triples) that was shown in Tzouvaras (2007) [5] to be equivalent to the consistency of NF. Such weak versions were introduced in Tzouvaras (2009) [6] in order to relax the intractability of the original condition. The result strengthens one of the main theorems of Tzouvaras (2007) [5, Theorem 3.6] which is just equivalent to the 〈0,0,2〉-property. 相似文献
7.
A metric space (X,d) has the Haver property if for each sequence ?1,?2,… of positive numbers there exist disjoint open collections V1,V2,… of open subsets of X, with diameters of members of Vi less than ?i and covering X, and the Menger property is a classical covering counterpart to σ-compactness. We show that, under Martin's Axiom MA, the metric square (X,d)×(X,d) of a separable metric space with the Haver property can fail this property, even if X2 is a Menger space, and that there is a separable normed linear Menger space M such that (M,d) has the Haver property for every translation invariant metric d generating the topology of M, but not for every metric generating the topology. These results answer some questions by L. Babinkostova [L. Babinkostova, When does the Haver property imply selective screenability? Topology Appl. 154 (2007) 1971-1979; L. Babinkostova, Selective screenability in topological groups, Topology Appl. 156 (1) (2008) 2-9]. 相似文献
8.
Roman Pol 《Topology and its Applications》2010,157(8):1506-1509
Assuming Martin's axiom MA, we define a homeomorphism between two strong measure zero sets in the real line whose graph in not of strong measure zero in the plane. Using Michael's concentrated sets, we give also some refinements of this result, and we describe some singular subgroups of the group ZN. 相似文献
9.
Camillo Costantini 《Topology and its Applications》2007,154(8):1726-1736
We prove that under a=c (in particular, under Martin's Axiom) there exists a regular σ-compact sequential space which is not hereditarily weakly Whyburn. This gives a consistent solution to a question, first formulated by V.V. Tkachuk and I.V. Yashenko, and then raised again by F. Obersnel. 相似文献
10.
Masami Sakai 《Topology and its Applications》2012,159(1):308-314
Let F[X] be the Pixley-Roy hyperspace of a regular space X. In this paper, we prove the following theorem.
Theorem.
For a space X, the following are equivalent:
- (1)
- F[X]is a k-space;
- (2)
- F[X]is sequential;
- (3)
- F[X]is Fréchet-Urysohn;
- (4)
- Every finite power of X is Fréchet-Urysohn for finite sets;
- (5)
- Every finite power ofF[X]is Fréchet-Urysohn for finite sets.
11.
This paper concerns the model of Cummings and Foreman where from ω supercompact cardinals they obtain the tree property at each ℵn for 2≤n<ω. We prove some structural facts about this model. We show that the combinatorics at ℵω+1 in this model depend strongly on the properties of ω1 in the ground model. From different ground models for the Cummings–Foreman iteration we can obtain either ℵω+1∈I[ℵω+1] and every stationary subset of ℵω+1 reflects or there are a bad scale at ℵω and a non-reflecting stationary subset of ℵω+1∩cof(ω1). We also prove that regardless of the ground model a strong generalization of the tree property holds at each ℵn for n≥2. 相似文献
12.
We correct the statement and the proof of Proposition 9 in [D. Bonheure, M. Ramos, Multiple critical points of perturbed symmetric strongly indefinite functionals, http://dx.doi.org/10.1016/j.anihpc.2008.06.002]. 相似文献
13.
14.
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
15.
This article deals with Leibniz's reception of Descartes' “geometry.” Leibnizian mathematics was based on five fundamental notions: calculus, characteristic, art of invention, method, and freedom. On the basis of methodological considerations Leibniz criticized Descartes' restriction of geometry to objects that could be given in terms of algebraic (i.e., finite) equations: “Descartes's mind was the limit of science.” The failure of algebra to solve equations of higher degree led Leibniz to develop linear algebra, and the failure of algebra to deal with transcendental problems led him to conceive of a science of the infinite. Hence Leibniz reconstructed the mathematical corpus, created new (transcendental) notions, and redefined known notions (equality, exactness, construction), thus establishing “a veritable complement of algebra for the transcendentals”: infinite equations, i.e., infinite series, became inestimable tools of mathematical research. 相似文献
16.
Magdy Assem 《manuscripta mathematica》1996,89(1):267-279
We prove that if rational measures are used on p-adic reductive groups then the orbital integrals of any given smooth and
compactly supported complex valued function belong to the field generated by the values of that function. We also show that
the Shalika germs are then rational valued functions. As a consequence, we are able to show, in certain cases, that the coefficients
appearing in the Harish-Chandra local character expansion are rational numbers.
Research supported by NSERC 相似文献
17.
We show that two versions of a first countable topological space which are equivalent in ZFC set theory split in the absence of the Axiom of Choice AC. This answers in the negative a related question from Gutierres “What is a first countable space?”. 相似文献
18.
Masaru Kada 《Topology and its Applications》2007,154(1):277-281
A slalom is a sequence of finite sets of length ω. Slaloms are ordered by coordinatewise inclusion with finitely many exceptions. Improving earlier results of Mildenberger, Shelah and Tsaban, we prove consistency results concerning existence and non-existence of an increasing sequence of a certain type of slaloms which covers a bounded set of functions in ωω. 相似文献
19.
20.
Franklin D. Tall 《Topology and its Applications》2011,158(18):2556-2563
We discuss relationships in Lindelöf spaces among the properties “Menger”, “Hurewicz”, “Alster”, “productive”, and “D”. 相似文献