Abstract
I understand C. G. Jung to say that even the most subjective of all notions, psyche, has objective aspects buried in the collective unconscious [0]. If he is correct, then the notion of RE set, which has at least as many meanings as there are areas of logic, also has objective aspects in the ground common to all logicians. The most inspired account of the notion of RE sets was given by Post [1] in 1944. In his paper an RE set is a set that has an effective enumeration. Thus it is not to be thought of as a set defined by a Σ1 formula or as a semi-recursive set dependent on computations. Its most apparent feature is positive change. It increases in an effective manner, and is the limit of finite subsets developed along the way. This dynamic view has many consequences. For example RE sets obey an effective selection principle. An element of a non-empty RE set can be selected by simply enumerating the set until its first member appears. In addition complex RE sets can be constructed by enumerating all RE sets simultaneously and diagonalizing.
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© 1977 D. Reidel Publishing Company, Dordrecht, Holland
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Sacks, G.E. (1977). Re Sets Higher up. In: Butts, R.E., Hintikka, J. (eds) Logic, Foundations of Mathematics, and Computability Theory. The University of Western Ontario Series in Philosophy of Science, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1138-9_10
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DOI: https://doi.org/10.1007/978-94-010-1138-9_10
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