A term that describes high-order ordinal numbers

primary, secondary, tertiary, quaternary, quinary, senary, septenary, octonary, nonary, denary, duodenary, etc.

are ordinal numbers as answered in this question. However, I'm looking for a word/phrase that refers to these terms in general, as in the following sentence:

Are there any secondary or word_or_phrase equity offering from this company?

Currently I'm considering replacing word_or_phrase with higher-order, higher-tier or n-ary, with the intended meaning of "from tertiary onwards".

Any help will be much appreciated.

Solution 1:

When employing ordinal numbers you are explaining a relationship between items in a set. The term you use to describe those numbers will largely depend upon the items in the set.

For example: Primary care vs. Tertiary care. You would describe these levels as tiers. Hence, if there were quaternary care, etc. you would describe this as higher-tier.

If you are speaking of classes: First class, second class, etc. You would call these higher classed (and of course these would typically go in reverse order first being highest).

If you are speaking of orders: Tertiary, Quaternary, etc. You would call these higher-ordered.

And, in any case, if you wish to describe a portion of a set, you would typically define your terms: e.g. Higher-ordered thingamajigs (Quaternary and beyond).

Of course, given that order is within the base definition and etymology of ordinal, I would say high(er)-order is always superficially correct.