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1.
We isolate several classes of stationary sets of [k]ωand investigate implications among them. Under a large cardinal assumption, we prove a structure theorem for stationary sets. 相似文献
2.
We construct a generic extension in which the ℵ2nd canonical function on ℵ1 exists.
Supported by NSF and by a Fulbright grant.
Publ. 378. Partially supported by the B.S.F. 相似文献
3.
A simple radioactive labeling technique is described which is based on a recoil injection of atoms of222Rn and its decay products from a226Ra source into thin surface layers of solids. 相似文献
4.
Let be a singular cardinal of regular uncountable cofinality. Let {(): < } be a continuous increasing sequence withlimit , and let =()+(), < be regular cardinals. Let I be a normal ideal on , and assume that the reduced product</I admits a cofinal -scale of ordinal functions. Then +, where =||||I is the I-norm of . 相似文献
5.
For every regular cardinal there exists a simple complete Boolean algebra with generators.
6.
Let be an inaccessible cardinal, and let and is regular and . It is consistent that the set is stationary and that every stationary subset of reflects at almost every .
7.
We consider algebras with one binary operation · and one generator (monogenic) and satisfying the left distributive lawa·(b·c)=(a·b)·(a·c). One can define a sequence of finite left-distributive algebrasAn, and then take a limit to get an infinite monogenic left-distributive algebraA∞. Results of Laver and Steel assuming a strong large cardinal axiom imply thatA∞is free; it is open whether the freeness ofA∞can be proved without the large cardinal assumption, or even in Peano arithmetic. The main result of this paper is the equivalence of this problem with the existence of a certain algebra of increasing functions on natural numbers, called anembedding algebra. Using this and results of the first author, we conclude that the freeness ofA∞is unprovable in primitive recursive arithmetic. 相似文献
8.
Let B be a complete ccc Boolean algebra and let s be the topologyon B induced by the algebraic convergence of sequences in B.
- Either there exists a Maharam submeasure on B or every nonemptyopen set in (B, s) is topologically dense.
- It is consistentthat every weakly distributive complete cccBoolean algebracarries a strictly positive Maharam submeasure.
- The topologicalspace(B, s) is sequentially compact if and onlyif the genericextension by B does not add independent reals.
9.
T. Jech 《Israel Journal of Mathematics》1968,6(4):363-367
It is shown that ifZF + the axiom of choice + “there is a measurable cardinal” is consistent thenZF + “ω
1 is measurable” is consistent. The corresponding model is a symmetric submodel of the Cohen-type extension which collapses
the first measurable cardinal onto ω0. 相似文献
10.
Projective Stationary Sets and a Strong Reflection Principle 总被引:1,自引:0,他引:1
The paper studies projective stationary sets. The ProjectiveStationary Reflection Principle is the statement that everyprojective stationary set contains an increasing continuous-chain of length 1. It is shown that, if Martin's Maximum holds,then the Projective Stationary Reflection Principle holds. Also,this principle is equivalent to the Strong Reflection Principle.The paper shows that the saturation of the nonstationary idealon 1 is equivalent to a certain kind of reflection. 相似文献