Annals of Mathematical Logic最新文献

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Recursive models for constructive set theories 构造集理论的递归模型

Annals of Mathematical Logic

Pub Date : 1982-12-01 DOI: 10.1016/0003-4843(82)90003-1

M. Beeson

We define recursive models of Martin-Löf's (type or) set theories. These models are a sort of recursive realizability; in fact, we show that for implication-free formulae of HA^ω, satisfaction in the model coincides with mr-HEO realizability. Using an idea of Aczel, we extend the model to a recursive model of the constructive set theories of Myhill and Friedman. Our models can be described without presupposing any knowledge of Martin-Löf's theories, and may make them seem less mysterious. We use our models to obtain several metamathematical results, for example consistency and independence results concerning continuity of functions on compact metric spaces. On the other hand, Martin-Löfs (latest) theories refute continuity of functions from N^N to N, as well as Church's thesis, although a show that all provably well-defined functions are continuous.

我们定义了Martin-Löf的(类型或)集合论的递归模型。这些模型是一种递归可实现性;事实上，我们证明了对于HAω的无隐含公式，模型的满意度与mr-HEO的可实现性一致。利用Aczel的思想，我们将该模型扩展为Myhill和Friedman的构造集理论的递归模型。我们的模型可以在不预先假定任何Martin-Löf理论知识的情况下描述，并且可能使它们看起来不那么神秘。我们利用我们的模型得到了一些元数学结果，例如紧度量空间上函数连续性的一致性和独立性结果。另一方面，Martin-Löfs(最新)理论驳斥了函数从NN到N的连续性，以及Church的论文，尽管a表明所有可证明定义良好的函数都是连续的。

引用次数: 45

Morasses, diamond, and forcing 沼泽，钻石，强迫

Annals of Mathematical Logic

Pub Date : 1982-12-01 DOI: 10.1016/0003-4843(82)90005-5

Daniel J. Velleman

引用次数: 48

A very absolute Π21 real singleton 一个非常绝对的Π21真正的单身

Annals of Mathematical Logic

Pub Date : 1982-12-01 DOI: 10.1016/0003-4843(82)90001-8

René David

引用次数: 16

Δ31 reals Δ31个实数

Annals of Mathematical Logic

Pub Date : 1982-12-01 DOI: 10.1016/0003-4843(82)90002-X

René David

引用次数: 1

Monadic theory of order and topology in ZFC ZFC中单元序和拓扑理论

Annals of Mathematical Logic

Pub Date : 1982-12-01 DOI: 10.1016/0003-4843(82)90004-3

Yuri Gurevich, Saharon Shelah

True first-order arithmetic is interpreted in the monadic theories of certain chains and topological spaces including the real line and the Cantor Discontinuum. It was known that existence of such interpretations in consistent with ZFC.

在某些链和拓扑空间(包括实线和康托非连续统)的一元理论中解释了真一阶算法。众所周知，这种解释的存在与ZFC是一致的。

引用次数: 41

Concepts of general topology in constructive mathematics and in sheaves, II 构造数学中一般拓扑学的概念，2

Annals of Mathematical Logic

Pub Date : 1982-10-01 DOI: 10.1016/0003-4843(82)90010-9

R.J. Grayson

Topological properties of spaces of sections of bundles are investigated in detail, and connected with results in constructive topology, in particular for notions of compactness, connectedness and uniformity.

详细研究了束的截面空间的拓扑性质，并与构造拓扑的结果联系起来，特别是紧性、连通性和均匀性的概念。

引用次数: 28

The Boolean algebra of formulas of first-order logic 一阶逻辑公式的布尔代数

Annals of Mathematical Logic

Pub Date : 1982-10-01 DOI: 10.1016/0003-4843(82)90009-2

Don H. Faust

The algebraic and recursive structure of countable languages of classical first-order logic with equality is analysed. All languages of finite undecidable similarity type are shown to be algebraically and recursively equivalent in the following sense: their Boolean algebras of formulas are, after trivial involving the one element models of the languages have been excepted, recursively isomorphic by a map which preserves the degree of recursiveness of their models.

分析了经典一阶逻辑等价可数语言的代数和递归结构。所有有限不可判定相似类型的语言在以下意义上都是代数和递归等价的:它们的布尔代数公式，除了涉及语言的单元素模型之外，通过保留其模型递归程度的映射递归同构。

引用次数: 8

Decidability and stability of free nilpotent lie algebras and free nilpotent p-groups of finite exponent 自由幂零李代数和有限指数的自由幂零p群的可决性和稳定性

Annals of Mathematical Logic

Pub Date : 1982-10-01 DOI: 10.1016/0003-4843(82)90008-0

Andreas Baudisch

Our main result is the decidability and ω-stability of free cth nilpotent p-groups of finite exponent (c < p).

我们的主要结果是有限指数(c <)的自由幂零p群的可判定性和ω-稳定性。p)。

引用次数: 18

A correction to “concepts of general topology in constructive mathematics and in sheaves” 对“构造数学中的一般拓扑学概念和束”的修正

Annals of Mathematical Logic

Pub Date : 1982-10-01 DOI: 10.1016/0003-4843(82)90011-0

R.J. Grayson

引用次数: 0

On the completenes principle: A study of provability in heyting's arithmetic and extensions 完备原理:heyting算法及其扩展的可证明性研究

Annals of Mathematical Logic

Pub Date : 1982-08-01 DOI: 10.1016/0003-4843(82)90024-9

Albert Visser

In this paper extensions of HA are studied that prove their own completeness, i.e. they prove A → □ A, where □ is interpreted as provability in the theory itself. Motivation is three-fold: (1) these theories are thought to have some intrinsic interest, (2) they are a tool for producing and studying provability principles, (3) they can be used to proved independence results. Work done in the paper connected with these motivations is respectively:

1.
(i) A characterization is given of theories proving their own completeness, including an appropriate conservation result.
2.
(ii) Some new provability principles are produced. The provability logic of HA is not a sublogic of the of PA. A provability logic plus completeness theorem is given for a certain intuitionistic extension of HA. De Jongh's theorem for propositional logic is a corollary.
3.
(iii) FP-realizability in Beeson's proof that $∦_{HA}$ KLS is replaced by theories proving their own completeness. New consequences are $∦_{HA+−M_{PR}} KLS$ , $∦_{HA+DNS} KLS$ .

本文研究了证明自身完备性的HA的扩展，即证明了A→□A，其中□被解释为理论本身的可证明性。动机有三个方面:(1)这些理论被认为具有某种内在的利益，(2)它们是产生和研究可证明性原则的工具，(3)它们可用于证明独立性的结果。本文所做的与这些动机有关的工作分别是:1.(i)给出了证明其完备性的理论的一个表征，包括一个适当的守恒结果。2.(ii)给出了一些新的可证明性原理。HA的可证明性逻辑不是PA的子逻辑。对于HA的某一直觉扩展，给出了一个可证性逻辑加完备性定理。3.(iii) Beeson证明∦HA KLS被证明其自身完备性的理论所取代的fp -可实现性。新的结果是∦HA+−MPR KLS，∦HA+DNS KLS。

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引用次数: 53

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