= Solution
\b[No.] <Universal sentences> are preserved under <substructure of a first-order structure>[substructures]. Every infinite $K$-vector space has its zero subspace as an $L$-substructure, since zero is named and every <scalar multiplication> preserves it. This one-element structure is not infinite and is not a <first-order model>[model] of $T$. Thus the <first-order model>[model] class is not closed under <substructure of a first-order structure>[substructures] and has no universal axiomatization, even relative to the vector-space <axioms>.
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