Geodesic
Probabilistic canonical systems
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part V, Tome 32 (1972), pp. 66-76

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The Post's canonical systems with probabilistic measure on inferences are considered. The sets of words derivable with probability ${}>\lambda$ ($\lambda\operatorname{real}$) are investigated. The relations of those sets to the set of all derivable words are studied. Sufficient conditions are stated for the convergence to 1 of the probability to derive any derivable word when number of trials is increased. 
@article{ZNSL_1972_32_a9,
     author = {S. Yu. Maslov and E. D. Rusakov},
     title = {Probabilistic canonical systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {66--76},
     publisher = {mathdoc},
     volume = {32},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1972_32_a9/}
}
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S. Yu. Maslov; E. D. Rusakov. Probabilistic canonical systems. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part V, Tome 32 (1972), pp. 66-76. http://geodesic.mathdoc.fr/item/ZNSL_1972_32_a9/