The variety generated by the 3-element semiring S7 has exactly six finitely based subvarieties and contains a continuum of subvarieties, so S7 is of type 2^aleph0.
The finite basis problem for additively idempotent semirings of order four, I
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We study the finite basis problem for 4-element additively idempotent semirings whose additive reducts are semilattices of height 1. Up to isomorphism, there are 58 such algebras. We show that 49 of them are finitely based and the remaining ones are nonfinitely based.
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The finite basis problem for additively idempotent semirings that relate to S_7
The variety generated by the 3-element semiring S7 has exactly six finitely based subvarieties and contains a continuum of subvarieties, so S7 is of type 2^aleph0.