Abstract
An undecidable generable subset can be constructed for an arbitrary aggregate X. From the philosophical point of view this fact clarifies the relation between the notions of decidability and generability. Namely there is a calculus such that there is no algorithm to decide whether an arbitrary element of X can be generated by this calculus. On the other hand, from the practical point of view it is remarkable that all decision problems (i.e. problems of constructing of decision algorithms) naturally arising in mathematical practice are decision problems for generable sets (of course in the theory of algorithms and calculuses as well as in mathematical logic there are also decision problems of a different, more complicated type).
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© 1993 Springer Science+Business Media Dordrecht
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Uspensky, V., Semenov, A. (1993). Construction of an undecidable generable set. In: Algorithms: Main Ideas and Applications. Mathematics and Its Applications, vol 251. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8232-2_13
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DOI: https://doi.org/10.1007/978-94-015-8232-2_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4256-9
Online ISBN: 978-94-015-8232-2
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