Countable vector spaces with recursive operations Part II 1

Publisher： Cambridge University Press

E-ISSN： 1943-5886|36|3|477-493

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.36, Iss.3, 1971-09, pp. : 477-493

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Abstract

We use the same terminology and notations as in Part I of this paper [3], but numerals in square brackets refer to the references at the end of the present part. The word “space” will be used in the sense of “subspace of ŪF”. A. G. Hamilton [6] proved that any two α-bases of any α-space are recursively equivalent (see also [5]). This means that dim α V, introduced in [3] only for an isolic α-space V, can be defined for any α-space V. Several results of [3] can therefore be strengthened. These and some other improvements are listed in §8. It is proved in §9 that every α-subspace of an isolic α-space is again an isolic α-space.

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