Formal Theories for Transfinite Iterations of Generalized Inductive Definitions and Some Subsystems of Analysis
作者： Solomon Feferman
DOI: 10.1016/S0049-237X(08)70761-4
关键词: Transfinite number 、 Notation 、 Set (abstract data type) 、 Computability theory 、 Algebra 、 Bounded function 、 Arithmetic function 、 Mathematics 、 Iterated function 、 Natural number
摘要: Publisher Summary This chapter discusses the formal theories for transfinite iterations of generalized inductive definitions and some subsystems analysis. The first order systems express a principle defining specific sets natural numbers can be iterated υ times. in language classical analysis (containing variables numbers) roughly that there are hierarchies obtained by iterating hyperjump operation any number less than An arithmetic formula is one without set quantifiers or constants; it may contain parameters. arithmetical which all bounded said to elementary. usual notations recursion theory used formally informally. These special cases Kreisel's results concerning intuitionistic systems. suggests definite technical advantages reductions limitations their foundational significance.
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