The theory of functions and sets of natural numbers
The theory of functions and sets of natural numbers
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发表时间：
1989
影响因子：
0.5
通讯作者：
P. Odifreddi
中科院分区：
文献类型：
--
作者：
P. Odifreddi
递归性和可计算性。入职。方程组。算术形式系统图灵机流程图。作为规则的功能。算术化。教堂的论文。基本递归理论部分递归函数对角化。部分递归函数。有效的操作。索引和枚举。可回溯集和回归集。Post问题和强可约性。Post的问题。简单集和多1度。超单集与真值表度超超单集和Q-度解决Post的问题。创造性和完整性。递归同构类型。真值表归约的变体。成套的世界。形式系统与RE集.层次结构和弱可约性。算术层次。层次分析法。集合论层次结构。可构建的层次结构。图灵度程度理论的语言。有限延拓方法Baire类别。Coinfinite扩展方法树的方法。初始分段。环球地产。跳跃度理论。多个一和其他学位。分配性。可计数的初始段。无数的初始段。环球地产。度理论的比较。度内结构。参考书目。指数.
Recursiveness and Computability. Induction. Systems of Equations. Arithmetical Formal Systems. Turing Machines. Flowcharts. Functions as Rules. Arithmetization. Church's Thesis. Basic Recursion Theory. Partial Recursive Functions. Diagonalization. Partial Recursive Functionals. Effective Operations. Indices and Enumerations. Retraceable and Regressive Sets. Post's Problem and Strong Reducibilities. Post's Problem. Simple Sets and Many-One Degrees. Hypersimple Sets and Truth-Table Degrees. Hyperhypersimple Sets and Q-Degrees. A Solution to Post's Problem. Creative Sets and Completeness. Recursive Isomorphism Types. Variations of Truth-Table Reducibility. The World of Complete Sets. Formal Systems and R.E. Sets. Hierarchies and Weak Reducibilities. The Arithmetical Hierarchy. The Analytical Hierarchy. The Set-Theoretical Hierarchy. The Constructible Hierarchy. Turing Degrees. The Language of Degree Theory. The Finite Extension Method. Baire Category. The Coinfinite Extension Method. The Tree Method. Initial Segments. Global Properties. Degree Theory with Jump. Many-One and Other Degrees. Distributivity. Countable Initial Segments. Uncountable Initial Segments. Global Properties. Comparison of Degree Theories. Structure Inside Degrees. Bibliography. Index.