Abstract
The continuous or countable functionals form a class of objects which are finitely approximable — they can be completely described by a set of (hereditarily) finite sets (approximations). We introduce and study a wider class of objects — sets, functions, and relations — all of which lay claim to a notion of finite approximability.
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References
Dugundji, J., Topology, Allyn and Bacon, Boston, 1966, xvi + 447 pp.
Hinman, P.G., Recursion-Theoretic Hierarchies, Perspectives in Mathematical Logic, Springer-Verlag, Berlin-Heidelberg-New York, 1978, xii + 480 pp.
Hyland, J.M.E., Filter spaces and continuous functionals, Annals of Mathematical Logic 16 (1979) 101–143.
Kechris, A.S. and Moschovakis, Y.N., Recursion in higher types, Handbook of Mathematical Logic, ed. K.J. Barwise, North-Holland, Amsterdam, 1977, 681–737.
Kleene, S.C., Countable functionals, Constructivity in Mathematics, ed. A. Heyting. North-Holland, Amsterdam, 1959, 81–100.
Kreisel, G., Interpretation of analysis by means of functionals of finite type, Constructivity in Mathematics, ed. A. Heyting, North-Holland, Amsterdam, 1959, 101–128.
Normann, D., Set recursion, Generalized Recursion Theory II, ed. J.E. Fenstad, R.O. Gandy, and G.E. Sacks, North-Holland, Amsterdam, 1978, 303–320.
Normann, D., Recursion on the countable functionals, Lecture Notes in Mathematics 811, Springer-Verlag, Berlin-Heidelberg-New York, 1980, viii + 191 pp.
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Hinman, P.G. (1984). Finitely approximable sets. In: Börger, E., Oberschelp, W., Richter, M.M., Schinzel, B., Thomas, W. (eds) Computation and Proof Theory. Lecture Notes in Mathematics, vol 1104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099488
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DOI: https://doi.org/10.1007/BFb0099488
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