Contents

• Introduction
• The landscape: Interpretability
  • The formalization of interpretability
  • Valid arithmetical principles
  • The other principles
• The modal logic of interpretability
  • The basic interpretability logic
  • More principles and frame correspondences
  • Modal and arithmetical completeness results
  • The aim of this paper
• The modal completeness and decidability of $\mathit{ILM}$ via the construction method
  • The general construction of the proof
  • Tools
  • The construction
• The modal completeness of $\mathit{ILM_0}$ via the construction method
  • General outline of the proof
  • Tools
  • The construction
  • Some remarks on decidability
• A new principle
  • The birth of a new principle: P₀
  • The enclosure of $\mathit{GIL}$
  • Independence results concerning P₀
  • A relation between M₀ and W
  • The arithmetical validity of P₀
• Concluding
  • The new situation
  • Spin off
  • Further research
• Acknowledgments
• Contents
• Bibliography