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)
“Stories of law violations are weighed on a different set of scales in the Black mind than in the white. Petty crimes embarrass the community and many people wistfully wonder why Negroes don’t rob more banks, embezzle more funds and employ graft in the unions.... This ... appeals particularly to one who is unable to compete legally with his fellow citizens.”
—Maya Angelou (b. 1928)
“The theory of rights enables us to rise and overthrow obstacles, but not to found a strong and lasting accord between all the elements which compose the nation.”
—Giuseppe Mazzini (1805–1872)