  We study influence of ordinal transformations on results of queries in
rank-aware databases which derive their operations with ranked relations from
totally ordered structures of scores with infima acting as aggregation
functions. We introduce notions of ordinal containment and equivalence of
ranked relations and prove that infima-based algebraic operations with ranked
relations are invariant to ordinal transformations: Queries applied to original
and transformed data yield results which are equivalent in terms of the order
given by scores, meaning that top-k results of queries remain the same. We show
this important property is preserved in alternative query systems based of
relational calculi developed in context of G\"odel logic. We comment on
relationship to monotone query evaluation and show that the results can be
attained in alternative rank-aware approaches.
