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In the field of logic and set theory, American mathematician and philosopher Solomon Feferman developed explicit mathematics, which is a collection of axiomatic systems related to constructive mathematics. It refers to a set of fundamental logical systems based on mathematical logic. A second type of class is added to a first-order logic of partial terms axiomatizing combinatory algebra. Alternative names: classifications, or types are sometimes used. The aim of explicit mathmetics was to have a straightforward and principled transfer of the notions of indescribable cardinals from set theory to admissible ordinals, yet the approach leaves open the question as to what is the proper analogue for admissible ordinals — if any — of a cardinal κ being [math]\displaystyle{ \Pi^m_n }[/math]-indescribable for m > 1.