Abstract:
A definition is provided of $k$-fold infinite sums and products of isol integers, and certain properties of such sums and products are proven. The definition is based on the concept of generalized recursive equivalence types, introduced at the beginning of this paper. The validity of the properties, connected with the canonical extensions of functions on isols, is established for arbitrary functions, and not only for general recursive functions, since the generalized recursive equivalence types permit their incorporation without the Nerode metatheorem in the proof of such properties.
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