1 Introduction

2 Global Degree Structures

3 Local Degree Structures

4 Implicative Lattices

5 Lattice Logics

6 Special Degrees

7 $\Pi_{1}^{0}$ Sets and Classes

8 Proof of Theorem A

9 Proof of Theorem D

10 Proof of Theorem E

11 Proof of Theorem F

12 Proof of Theorem G

13 Proof of Theorem H

14-and-Completeness Theorems

15 Proof of Theorem I

16 Proof of Theorem K