In the spirit of constructing conditional events from events, there have been several proposals for constructing conditional conditional events from conditional events. There are many procedures for this that are analogous to the construction of conditional events from events, and many possible choices of operations to impose on the resulting sets. It is observed here that the Stone algebra of conditional events is actually a symmetric Stone algebra and that there is a natural construction of iterated conditionals extending the symmetric Stone algebra structure of conditional events. This new symmetric Stone algebra of iterated conditionals has a representation in which its operations ar
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