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Characterizing the continuous functionals. (English) Zbl 0536.03026

The continuous functionals as defined by Kleene and Kreisel are in some sense a completion of the finitary functionals. In this paper one takes the standard part of the hyperfinitary functionals in some non-standard elementary extension, and shows that these standard parts form the continuous functionals. This justifies the term completion.

MSC:

03D65 Higher-type and set recursion theory
03H10 Other applications of nonstandard models (economics, physics, etc.)
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References:

[1] Constructivity in Mathematics pp 101– (1959)
[2] DOI: 10.1007/BF01463138 · Zbl 0325.02027 · doi:10.1007/BF01463138
[3] DOI: 10.1016/0003-4843(79)90006-8 · Zbl 0415.03037 · doi:10.1016/0003-4843(79)90006-8
[4] Constructivity in Mathematics pp 81– (1959)
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