Order Theory and Lattice Theory Synonymous?

Question

Is Order Theory the same as Lattice Theory?

Can anyone recommend good beginners text book on either?

Answer 1

I learned the basics from Introduction to Lattices and Order, 2nd Edition, by B. A. Davey and H. A. Priestley. Its not bad. To answer your title question: technically, order theory is more general than lattice theory. In practice you don't really study one without also studying the other.

Answer 2

Not exactly synonyms order theory is broader than lattice theory. Lattice theory studies the algebraic structure, lattices, whereas order theory is the general study of binary relations, including partially ordered sets, total orders, and lattices.

For a book on LT, I recommend 'Lattice Theory with Applications' by V. K. Garg.

Answer 3

I know this is older but a good recent reference and text I discovered was "Lattices and Ordered Sets" by Steve Roman. He also has some YouTube videos where he goes over some related material.