sequent

Meanings

1. 1
   noun

   in proof theory, a formal expression showing that one or more conclusion formulas follow from a collection of premise formulas

   The sequent places the assumptions to the left of the turnstile and the conclusion to its right.

2. 2
   noun

   in Russell's order theory, a minimal member among the successors of a class with respect to a relation

   If the ordered class has a least upper successor, that term is its sequent.

3. 3
   adj

   following next in time, order, or consequence

   Each night was followed by a sequent day.

Borrowed in the sixteenth century through Middle French sequent from Latin sequent-, the stem of sequens ("following"), present participle of sequi ("to follow"). Its modern proof-theory noun sense names a formal consequence statement; Russell used the noun for a particular successor of an ordered class.

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