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- W986903923 abstract "This chapter discusses the contribution of Mostowski to the foundations of second order arithmetic. Second order arithmetic is a theory of irrational numbers. Systematic work on the foundations of this theory began in mid-fifties, when Mostowski published paper 62. Besides a precise description of the system of second order arithmetic and its syntactical rules the paper contains a beautiful topological proof of Grey's theorem. Some connections with theory of recursive functions are considered and some similarities between particular classes of effective hierarchy are emphasized. The fundamental work on the subject is the “Formal system of analysis based on an infinitistic rule of proof” presented by Mostowski at the Warsaw “Infinitistic Methods” Symposium in 1959. This paper introduces the important notion of models absolute for well orderings of natural numbers. The problem of the existence of ω-models which are not β-models is discussed in a joint paper by Mostowski and Suzuki. Paper 103 imposes a naturally defined partial ordering of encodable membership on the family of ω-models. Paper 102 discusses the problem of definability of Skolem functions." @default.
- W986903923 created "2016-06-24" @default.
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- W986903923 date "1979-01-01" @default.
- W986903923 modified "2023-09-27" @default.
- W986903923 title "The contribution of Mostowski to the foundations of second order arithmetic" @default.
- W986903923 doi "https://doi.org/10.1016/s0049-237x(09)70454-9" @default.
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