The Structure of Detour Degrees

Kristiansen, Lars; Voda, Paul J.

doi:10.1007/978-3-540-79228-4_13

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“…Recently, argument-bounded idc's have found a new use in the context of detour degrees a la Kristiansen and Voda (see Kristiansen and Voda (2008)), and I expect that some of the results presented here will be very useful in the further development of that theory.…”

Section: Introductionmentioning

confidence: 74%

Bounded minimalisation and bounded counting in argument-bounded idc's

Barra¹

2010

Math. Struct. Comp. Sci.

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We define and investigate a number of small inductively defined classes (idc's),à la Gregorczyk, that are based on argument-bounded initial functions and the bounded minimalisation and bounded counting schemata. We establish equivalences between these and other classes in the literature, with an emphasis on minimalism. We also obtain characterisations of the classes in terms of well-known fragments of first-order predicate logic. † In the expression, the '∃ w6max( x,y) '-quantifier is formal shorthand for the finite disjunction ∃ w6x 1 φ ∨ ∃ w6x k φ ∨ · · · ∨ ∃ w6y φ, which is a PrA-formula when φ is.

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Section: Introductionmentioning

confidence: 74%