Bases and α-dimensions of countable vector spaces with recursive operations 1

Publisher： Cambridge University Press

E-ISSN： 1943-5886|35|1|85-96

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.35, Iss.1, 1970-03, pp. : 85-96

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Abstract

This paper is based on the notions originally described by Dekker [2], [3], and the reader is referred to these for explanation of notation etc. Briefly, we are concerned with a countably infinite dimensional countable vector space Ū with recursive operations, regarded as being coded as a set of natural numbers. Necessarily, then, Ū must be a vector space over a field which itself is in some sense recursively enumerable and has recursive operations.

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