Examples Illustrating the Back-and-Forth Method

Abstract

The five examples in this chapter illustrate the method described in the previous chapter; they will also serve to provide examples for the rest of the course. The author does not claim that these are the most important applications of model theory to algebra or to other branches of mathematics, or the most fruitful, and he recognizes that he has chosen cases where the back-and-forth method applies particularly well.

Lors fu li conseils des barons telx que il se hebergeroient entre le palais de Blaquerne et le chastel Buimont, qui ere une abaîe close de murs. Et lors furent tendu li tref et li paveillon, et bien fu fiere chose a regarder: que de Constantinoble, qui tenoit III lieus de front par devers la terre, ne pot tote l’ost assegier que l’une des portes. ... Et mult estoient perillousement, que onques par tant poi de gent ne furent assegié tant de gent en nulle ville.

J. de V.