Fixed Point Theory in Weak Second-Order Arithmetic
Fixed Point Theory in Weak Second-Order Arithmetic
复制标题
弱二阶算术中的不动点理论
DOI：
10.1016/0168-0072(90)90068-d
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
Kazuyuki Tanaka
中科院分区：
文献类型：
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作者：
N. Shioji;Kazuyuki Tanaka
本文的目的是在二阶算术的一个相对较弱的子系统中发展与不动点定理有关的泛函分析的一部分。的兴趣已经很好地建立通过正在进行的计划，称为反向数学，其最终目标是回答以下问题：什么集合存在公理需要证明定理的普通数学？有关该计划的信息，请参见[6]、[7]、[15]、[16]。这里我们简要地描述了这个系统和另外两个相关的系统，即递归理解系统和递归归纳系统。这是最弱的系统，我们将考虑，但仍然强大到足以发展一些基本理论的连续函数和可数代数。该系统由
The purpose of this paper is to develop part of functional analysis concernedwith fixed point theorems within a relatively weak subsystem of second-orderarithmetic, known as. The interestofhas been well established through ongoing program, called Reverse Mathematics, whose ultimate goal is to answer the following question: What set existence axioms are needed toprove the theorems of ordinary mathematics? For information on the program, see [6],[7],[15],[16]. We here briefly describe the systemand two other related systems,.is the system of recursive comprehension andinduction. This is the weakest system we shall consider, but is still strong enough to develop some basic theory of continuous functions and countable algebras. The systemconsists