Right tightening

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Right tightening, all facts related to Right tightening) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

Definition

Symbol-free definition

Given a restriction formal expression or extension formal expression for a property, a right tightening of the expression is another formal expression for the same property with the same left side but with the right side stronger than before.

Definition with symbols

Given a restriction formal expression or extension formal expression for a property, say $a$ → $b$, a right tightening for the property is another expression $c$ ≤ $b$ such that $a$ → $c$ = $a$ → $b$.

Property theory

Maximal right tightening and right tight expressions

For any expression, there is a maximal right tightening, after which no further proper right tightening is possible. A restriction (respectively extension) formal expression for which no further tight tightening is possible is termed a right tight restriction formal expression (respectively right tight extension formal expression). The maximal right tightening operator is thus an idempotent operator on the collection of all restriction formal expressions and its image is the collection of right tight restriction formal expressions.