sentences:  Subsets of "M"(Г) closed under the operations provide further examples of near-semirings.Another example is the ordinals under the usual operations of ordinal arithmetic (here Clause 3 should be replaced with its symmetric form "c" · ("a" + "b") = "c" · "a" + "c" · "b".Strictly speaking, the class of all ordinals is not a set, so the above example should be more appropriately called a "class near-semiring".