Comparing hierarchies of total functionals
In this paper we consider two hierarchies of hereditarily total and continuous functionals over the reals based on one extensional and one intensional representation of real numbers, and we discuss under which asumptions these hierarchies coincide. This coincidense problem is equivalent to a stateme...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2005-10-01
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| Series: | Logical Methods in Computer Science |
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| Online Access: | https://lmcs.episciences.org/2268/pdf |
| Summary: | In this paper we consider two hierarchies of hereditarily total and
continuous functionals over the reals based on one extensional and one
intensional representation of real numbers, and we discuss under which
asumptions these hierarchies coincide. This coincidense problem is equivalent
to a statement about the topology of the Kleene-Kreisel continuous functionals.
As a tool of independent interest, we show that the Kleene-Kreisel functionals
may be embedded into both these hierarchies. |
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| ISSN: | 1860-5974 |