Transitive Models of Set Theory
Transitive classes are often used for construction of interpretations of set theory in itself, usually called inner models. The reason is that properties defined by bounded formulas are absolute for transitive classes.
A transitive set (or class) that is a model of a formal system of set theory is called a transitive model of the system. Transitivity is an important factor in determining the absoluteness of formulas.
In the superstructure approach to non-standard analysis, the non-standard universes satisfy strong transitivity, see (Goldblatt, 1998, p.161).
Read more about this topic: Transitive Set
Famous quotes containing the words models, set and/or theory:
“Friends broaden our horizons. They serve as new models with whom we can identify. They allow us to be ourselves—and accept us that way. They enhance our self-esteem because they think we’re okay, because we matter to them. And because they matter to us—for various reasons, at various levels of intensity—they enrich the quality of our emotional life.”
—Judith Viorst (20th century)
“I hate the whole race.... There is no believing a word they say—your professional poets, I mean—there never existed a more worthless set than Byron and his friends for example.”
—Arthur Wellesley, 1st Duke Wellington (1769–1852)
“Every theory is a self-fulfilling prophecy that orders experience into the framework it provides.”
—Ruth Hubbard (b. 1924)