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In this work we introduce a class of commutative rings whose defining condition is that its lattice of ideals, augmented with the ideal product, the semi-ring of ideals, is isomorphic to an MV-algebra. This class of rings coincides with the class of commutative rings which are direct sums of local Artinian chain rings with unit.
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## Indestructibility and stationary reflection If ฮบ < ฮป are such that ฮบ is a strong cardinal whose strongness is indestructible under ฮบ-strategically closed forcing and ฮป is weakly compact, then we show that A = {ฮด < ฮบ | ฮด is a non-weakly compact Mahlo cardinal reflecting stationary sets} must be
Various types of continuity for preference relations on a metric space are examined constructively. In particular, necessary and sufficient conditions are given for an order-dense, strongly extensional preference relation on a complete metric space to be continuous. It is also shown, in the spirit o