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- W54536442 abstract "Publisher Summary This chapter discusses model-theoretic invariants and applications to Recursive and hyper-arithmetic operations. Both in informal mathematical reasoning and in foundations one sometimes identifies objects a and a' in two structures of the same similarity type whatever the ‘nature’ of the a , a' themselves may be. Thus, a mathematician does not distinguish between the rationale in one commutative field of characteristic 0 and any other. The principal general result establishes (for the case of general models) sharp explicit definability for each element of the common part. The most interesting applications come about through the following link with recursion theory. The class of recursive sets of natural numbers made its first appearance in the literature in Godel, not in connection with Church's problematic thesis, but under the name of ‘entscheidungs-definite Eigenschaften’. The principle involved in the applications is simply that familiar from ordinary mathematical analyses of concrete situations in abstract terms." @default.
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- W54536442 date "2014-01-01" @default.
- W54536442 modified "2023-09-26" @default.
- W54536442 title "MODEL-THEORETIC INVARIANTS: APPLICATIONS TO RECURSIVE AND HYPERARITHMETIC OPERATIONS" @default.
- W54536442 doi "https://doi.org/10.1016/b978-0-7204-2233-7.50025-3" @default.
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