Countable vector spaces with recursive operations Part II
- 1 September 1971
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 36 (3) , 477-493
- https://doi.org/10.2307/2269957
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 dimαV, introduced in [3] only for an isolic α-space V, can be defined for anyα-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.Keywords
This publication has 3 references indexed in Scilit:
- Two notes on vector spaces with recursive operations.Notre Dame Journal of Formal Logic, 1971
- Partial recursive functions and ω-functionsThe Journal of Symbolic Logic, 1970
- Countable vector spaces with recursive operations Part I1The Journal of Symbolic Logic, 1969