Proof-Oriented Categorical Semantics

Kapitel in diesem Buch

1. Frontmatter I
2. Preface V
3. Contents IX
4. Introduction 1
5. Herbrand Confluence for First-Order Proofs with Π₂-Cuts 5
6. Proof-Oriented Categorical Semantics 41
7. Logic for Gray-code Computation 69
8. The Continuum Hypothesis Implies Excluded Middle 111
9. Theories of Proof-Theoretic Strength Ψ (Γ_Ω +1) 115
10. Some Remarks about Normal Rings 141
11. On Sets of Premises 151
12. Non-Deterministic Inductive Definitions and Fullness 163
13. Cyclic Proofs for Linear Temporal Logic 171
14. Craig Interpolation via Hypersequents 193
15. A General View on Normal Form Theorems for Łukasiewicz Logic with Product 215
16. Relating Quotient Completions via Categorical Logic 229
17. Some Historical, Philosophical and Methodological Remarks on Proof in Mathematics 251
18. Cut Elimination in Sequent Calculi with Implicit Contraction, with a Conjecture on the Origin of Gentzen’s Altitude Line Construction 269
19. Hilbert’s Programme and Ordinal Analysis 291
20. Aristotle’s Deductive Logic: a Proof-Theoretical Study 323
21. Remarks on Barr’s Theorem: Proofs in Geometric Theories 347