Intro
Preface
Contents
1 Introduction
1.1 Convex Geometry
1.2 Krull Domains, Transfer Krull Monoids and Factorization
1.3 Zero-Sum Sequences
1.4 Overview of Main Results
2 Preliminaries and General Notation
2.1 Convex Geometry
2.2 Lattices and Partially Ordered Sets
2.3 Sequences and Rational Sequences
2.4 Arithmetic Invariants for Transfer Krull Monoids
2.5 Asymptotic Notation
3 Asymptotically Filtered Sequences, Encasement and Boundedness
3.1 Asymptotically Filtered Sequences
3.2 Encasement and Boundedness

4 Elementary Atoms, Positive Bases and Reay Systems
4.1 Basic Non-degeneracy Characterizations
4.2 Elementary Atoms and Positive Bases
4.3 Reay Systems
4.4 -Filtered Sequences, Minimal Encasement and Reay Systems
5 Oriented Reay Systems
6 Virtual Reay Systems
7 Finitary Sets
7.1 Core Definitions and Properties
7.2 Series Decompositions and Virtualizations
7.3 Finiteness Properties of Finitary Sets
7.4 Interchangeability and the Structure of X(G0)
8 Factorization Theory
8.1 Lambert Subsets and Elasticity
8.2 The Structure of Atoms and Arithmetic Invariants