de Finetti's coherence framework demonstrates that full additivity can be preserved by treating probability as a finitely additive measure without requiring countable additivity at all.

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Countable Additivity(Contested axiom in Bayesian epistemology and formal epistemology): A principle in probability theory stating that the probability of a countably infinite union of mutually exclusive events equals the sum of their individual probabilities
Finitely additive measure(as used in mathematics and logic): A mathematical rule for adding up quantities where if you break something into separate pieces, the total measurement of all pieces equals the measurement of the whole—like how the areas of two halves of a pizza add up to the whole pizza's area.
additivity (in probability)(a mathematical property being preserved in de Finetti's framework): The principle that when you combine probabilities of separate events, the total probability equals the sum of the individual probabilities.
coherence framework(de Finetti's main contribution to probability theory): A method for checking whether someone's beliefs about probabilities are consistent with each other—basically, a set of rules to make sure your probability estimates don't contradict themselves.

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