The Kolmogorov-Loveland stochastic sequences are not closed under selecting subsequences
Merkle, Wolfgang
J. Symbolic Logic, Tome 68 (2003) no. 1, p. 1362-1376 / Harvested from Project Euclid
It is shown that the class of Kolmogorov-Loveland stochastic sequences is not closed under selecting subsequences by monotonic computable selection rules. This result gives a strong negative answer to the question whether the Kolmogorov-Loveland stochastic sequences are closed under selecting sequences by Kolmogorov-Loveland selection rules, i.e., by not necessarily monotonic, partial computable selection rules. The following previously known results are obtained as corollaries. The Mises-Wald-Church stochastic sequences are not closed under computable permutations, hence in particular they form a strict superclass of the class of Kolmogorov-Loveland stochastic sequences. The Kolmogorov-Loveland selection rules are not closed under composition.
Publié le : 2003-12-14
Classification: 
@article{1067620192,
     author = {Merkle, Wolfgang},
     title = {The Kolmogorov-Loveland stochastic sequences are not closed
under selecting subsequences},
     journal = {J. Symbolic Logic},
     volume = {68},
     number = {1},
     year = {2003},
     pages = { 1362-1376},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1067620192}
}
Merkle, Wolfgang. The Kolmogorov-Loveland stochastic sequences are not closed
under selecting subsequences. J. Symbolic Logic, Tome 68 (2003) no. 1, pp.  1362-1376. http://gdmltest.u-ga.fr/item/1067620192/