[FOM] answer : : Fractional Iteration and Rates of Growth

[José Félix Costa]

Taranovsky:
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By using iteration, we can define natural functions with arbitrarily high
primitive recursive rate of growth, and an interesting question is whether
these functions have natural analogues defined at all positive real numbers.

My answer:
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We have several proofs of the existence of such extensions in our work
towards Kleene's theory of real recursive functions. In my webpage papers
can be found with such a theory.

Special attention to a Working Paper
http://fgc.math.ist.utl.pt/hierarchy.htm

and several publish papers in
http://fgc.math.ist.utl.pt/pubmajor.htm

This work have been developed since 1996 and about 6 persons are comnnected
with it, including me and Jerzy Mycka.

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J. Felix Costa
Departamento de Matematica
Instituto Superior Tecnico
Av. Rovisco Pais, 1049-001 Lisboa, PORTUGAL
tel:      351 - 21 - 841 71 45
fax:     351 - 21 - 841 75 98
e-mail:   fgc at math.ist.utl.pt
www:    http://fgc.math.ist.utl.pt/jfc.htm
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