Abstract
We take up the question of when a state (= σ-additive measure) on the product of logics (=σ-orthomodular posets) depends on at most countably many coordinates. We show that it is always so provided there are no real-measurable cardinals. The manner of dependence is a kind of convex combination. We derive some consequences of the latter statement.
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Maňasová, V., Pták, P. On states on the product of logics. Int J Theor Phys 20, 451–456 (1981). https://doi.org/10.1007/BF00671358
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DOI: https://doi.org/10.1007/BF00671358