Logic, Reasoning, and Knowledge
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Abstract
Abstract
We show that, in terms of closure ordinals, many infinitary calculi for “first-order” logics of probability (i.e., for languages similar to those in [M. Abadi and J. Y. Halpern, “Decidability and expressiveness for first-order logics of probability,” Inform. and Comput. 112 (1), 1–36, 1994] are as hard as possible: the corresponding closure ordinals coincide with the least nonconstructive ordinal, denoted by $$\omega_1^{\mathrm{CK}}$$ .
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@article{Speranski2026Closure,
title = {On the Closure Ordinals of Infinitary Probabilistic Calculi},
author = {S. O. Speranski},
journal = {Mathematical Notes},
year = {2026},
doi = {10.1134/s0001434626603850},
url = {https://doi.org/10.1134/s0001434626603850}
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