What is the correct term to describe the words in the following sequence: primary, secondary, tertiary, quaternary, quinary, senary, septenary, octonary, nonary, denary, duodenary, etc.
I am thinking '-tier' but I don't think I am correct.
I believe the words you have there are Latinate ordinal numbers.
From Wikipedia's Ordinal number (linguistics) article:
In linguistics, ordinal numbers are the words representing the rank of a number with respect to some order, in particular order or position (i.e. first, second, third, etc.). Its use may refer to size, importance, chronology, etc. ... They are different from the cardinal numbers (one, two, three, etc.) referring to the quantity. Ordinal numbers are alternatively written in English with numerals and letter suffixes: 1st, 2nd or 2d, 3rd or 3d, 4th, 11th, 21st, 101st, 477th, etc. ... Spatial or chronological ranks will use the standard linguistic ordinal numbers first, second, etc.; however, the ranking of precedence or effect often uses primary, secondary, etc. and historical rankings in literature, biology or music may use Greek prefixes, e.g., Proto-Isaiah, Deutero-Isaiah ...