Annals of Mathematical Logic最新文献

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On the length of Borel hierarchies 关于Borel层次结构的长度

Annals of Mathematical Logic

Pub Date : 1979-09-01 DOI: 10.1016/0003-4843(79)90003-2

Arnorld W. Miller

引用次数: 58

Degrees of functionals 泛函度

Annals of Mathematical Logic

Pub Date : 1979-09-01 DOI: 10.1016/0003-4843(79)90004-4

Dag Normann

In this paper we will discuss some problems of degree-theoretic nature in connection with recursion in normal objects of higher types.

Harrington [2] and Loewenthal [6] have proved some results concerning Post's problem and the Minimal Pair Problem, using recursion modulo subindividuals. Our degrees will be those obtained from Kleene-recursion modulo individuals. To solve our problems we then have to put some extra strength to ZFC. We will first assume V = L, and then we restrict ourselves to the situation of a recursive well-ordering and Martin's axiom.

We assume familiarity with recursion theory in higher types as presented in Kleene [3]. Further backround is found in Harrington [2], Moldestad [9] and Normann [11]. We will survey the parts of these papers that we need.

In Section 1 we give the general background for the arguments used later. In Section 2 we prove some lemmas assuming V = L. In section 3, assuming V = L we solve Post's problem and another problem using the finite injury method. We will thereby describe some of the methods needed for the more complex priority argument of Section 4 where we give a solution of the minimal pair problem for extended r.e. degress of functionals.

In Section 5 we will see that if Martin's Axiom holds and we have a minimal well-ordering of tp (1) recursive in ³E, we may use the same sort of arguments as in parts 3 and 4.

在本文中，我们将讨论与高等类型的普通对象的递归有关的一些程度论性质的问题。Harrington[2]和loeenthal[6]利用递归模子个体证明了Post问题和极小对问题的一些结果。我们的学位将是那些从kleene -递归模个体获得的学位。为了解决我们的问题，我们必须给ZFC增加一些额外的力量。我们首先假设V = L，然后我们将自己限制在递归良序和马丁公理的情况下。我们假设熟悉Kleene[3]中提出的高级类型的递归理论。在Harrington[2]、Moldestad[9]和Normann[11]中可以找到进一步的背景。我们将调查这些论文中我们需要的部分。在第1节中，我们将给出后面使用的参数的一般背景。在第2节中，我们证明了假设V = L的引理。在第3节中，假设V = L，我们用有限伤害法解决了Post问题和另一个问题。因此，我们将描述第4节中更复杂的优先级参数所需的一些方法，其中我们给出了泛函扩展r.e.度的最小对问题的解决方案。在第5节中，我们将看到，如果马丁公理成立，并且我们在3E中有最小的tp(1)递归良序，我们可以使用与第3部分和第4部分相同的参数。

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引用次数: 7

Filter spaces and continuous functionals 过滤空间和连续泛函

Annals of Mathematical Logic

Pub Date : 1979-07-01 DOI: 10.1016/0003-4843(79)90006-8

J.M.E. Hyland

引用次数: 90

Substructure lattices of models of arithmetic 算法模型的子结构格

Annals of Mathematical Logic

Pub Date : 1979-07-01 DOI: 10.1016/0003-4843(79)90007-X

George Mills

We completely characterize those distributive lattices which can be obtained as elementary substructure lattices of models of Peano arithmetic. Stated concisely: every plausible distributive lattice occurs abundantly. Our proof employs the notion of a strongly definable type in many variables. With slight modifications the method also yields a characterization of those distributive lattices which can be obtained uniformly by Gaifman's methods of definable and end extensional 1-types. As a special case this gives another proof of two conjectures involving finite distributive lattices and models of arithmetic posed by Gaifman and initially proved by Schmerl. We also show that every minimal type (in the sense of Gaifman) satisfies a strong partition property which we will call being “uniformly Ramsey”.

我们完整地刻画了那些可以作为Peano算法模型的初等子结构格的分配格。简明地说:每一个合理的分配格都大量出现。我们的证明在许多变量中使用了强可定义类型的概念。在稍作修改的情况下，该方法还得到了那些可定义型和可扩展1型的Gaifman方法所能统一得到的分布格的一个表征。作为一种特殊情况，本文给出了Gaifman提出并最初由Schmerl证明的涉及有限分配格和算术模型的两个猜想的另一个证明。我们还证明了每一个最小类型(在Gaifman意义上)都满足一个强划分性质，我们称之为“一致拉姆齐”。

引用次数: 8

Rosser sentences 伐木工人的句子

Annals of Mathematical Logic

Pub Date : 1979-05-01 DOI: 10.1016/0003-4843(79)90017-2

D. Guaspari , R.M. Solovay

引用次数: 0

Some applications of Kripke models to formal systems of intuitionistic analysis Kripke模型在直觉分析形式系统中的一些应用

Annals of Mathematical Logic

Pub Date : 1979-05-01 DOI: 10.1016/0003-4843(79)90014-7

Scott Weinstein

引用次数: 7

Regularity properties of ideals and ultrafilters 理想和超滤的正则性

Annals of Mathematical Logic

Pub Date : 1979-05-01 DOI: 10.1016/0003-4843(79)90015-9

Alan D. Taylor

For an arbitrary ideal I on the regular cardinal κ we consider the problem of refining a given collection ${A_{α} :α < κ}⊆ P (κ)−I$ by another collection ${B_{α} :α<κ}⊆ P (k)−I$ so that the sets in the latter collection are as nearly pairwise disjoint as possible. In this context we discuss regularity of ultrafilters, saturation of ideals and some problems of Fodor and Ulam.

对于正则基数κ上的任意理想I，我们考虑精炼给定集合{a α:α <{Bα:α<κ}相称于另一个集合{Bα:α<κ}相称于P(k)−I，使后一个集合中的集合尽可能接近成对不相交。在此背景下，我们讨论了超滤的正则性、理想饱和以及Fodor和Ulam的一些问题。

引用次数: 27

Finite injury arguments in infinite computation theories 无限计算理论中的有限损伤论证

Annals of Mathematical Logic

Pub Date : 1979-05-01 DOI: 10.1016/0003-4843(79)90016-0

V. Stoltenberg-Hansen

引用次数: 5

Finite injury arguments in infinite computation theories 无限计算理论中的有限损伤论证

Annals of Mathematical Logic

Pub Date : 1979-05-01 DOI: 10.1016/0003-4843(79)90016-0

Viggo Stoltenberg-Hansen

引用次数: 5

Generalized erdoös cardinals and O4 广义erdoös基数和O4

Annals of Mathematical Logic

Pub Date : 1978-12-01 DOI: 10.1016/0003-4843(78)90012-8

James E. Baumgartner , Fred Galvin

引用次数: 10

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