Some Model Theory of Free Groups and Free Algebras

摘要

The subject of this paper is group theory and logic with an emphasis on groups.The concept of a group is one of the most powerful and unifying of all concepts in mathematics. Moveover in addition to tuning up in every branch of mathematics, groups have endless applications in science. Wherever there is symmetry, there is a group. The Lorentz transformations of relativity from a Lie group based on continuous rotation of an object in space-time. Finite groups underlie the structure of all crystals and are indispensable in chemistry, quantum mechanics, and particle physics. The famous eight fold way, which classifies the family of subatomic particles known as hadrons, is a Lie group. In view of the great elegance and utility of groups, it is understandable that mathematicians study them and their properties, which is precisely what this paper does. There is, of course, no way to predict what other practical application this material will have. We do, however, know that groups lie at the very heart of the structure of the universe. group free algebra positive sentence free group universal formula