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:
“French rhetorical models are too narrow for the English tradition. Most pernicious of French imports is the notion that there is no person behind a text. Is there anything more affected, aggressive, and relentlessly concrete than a Parisan intellectual behind his/her turgid text? The Parisian is a provincial when he pretends to speak for the universe.”
—Camille Paglia (b. 1947)
“The Bostonians are really, as a race, far inferior in point of anything beyond mere intellect to any other set upon the continent of North America. They are decidedly the most servile imitators of the English it is possible to conceive.”
—Edgar Allan Poe (18091845)
“We commonly say that the rich man can speak the truth, can afford honesty, can afford independence of opinion and action;and that is the theory of nobility. But it is the rich man in a true sense, that is to say, not the man of large income and large expenditure, but solely the man whose outlay is less than his income and is steadily kept so.”
—Ralph Waldo Emerson (18031882)