Diener, Hannes: Constructive reverse mathematics : Habilitationsschrift. 2018
Inhalt
- Contents
- Chapter 0 - Introduction
- 0.1 Constructive Mathematics
- 0.2 Constructive Reverse Mathematics
- 0.3 A very Short History of Constructive Reverse Mathematics
- 0.4 Foundational Aspects
- 0.5 Overview and Plan
- Chapter 1 - Omniscience Principles
- Chapter 2 - MP and Below
- Chapter 3 - The Fan Theorems
- 3.1 Linking 2N and [0,1]
- 3.2 WWKL
- 3.3 FANΔ
- 3.4 FANc
- 3.5 UCT
- 3.6 FANn01 and FANstable
- 3.7 FANfull
- 3.8 Comparing the Fan Theorems
- Chapter 4 - BD-N and Below
- Chapter 5 - The recursive side
- Chapter 6 - Relationships Between the Principles
- 6.1 Basic Relations
- 6.2 Kripke's Schema and the Principle of Finite Possibility
- 6.3 Collapsing the Fan Theorems
- 6.4 Other Implications
- 6.5 The Big Picture
- Chapter 7 - Separating Principles
- Chapter 8 - Bits'n'Pieces
- 8.1 LLPOn
- 8.2 Open Induction
- 8.3 The Limited Anti-Specker Property
- 8.4 Increasing Specker Sequences
- 8.5 Dirk Gently's Principle
- 8.6 Π01 and Σ01
- 8.7 ¬WLPOand ¬LPO
- Appendix A - List of Open Questions
- Appendix B - Source Code
- Bibliography
- Index