You are here

Forcing with Random Variables and Proof Complexity

Jan Krajíček
Publisher: 
Cambridge University Press
Publication Date: 
2011
Number of Pages: 
247
Format: 
Paperback
Series: 
The London Mathematical Society Lecture Note Series 382
Price: 
65.00
ISBN: 
9780521154338
Category: 
Monograph
We do not plan to review this book.

Preface
Acknowledgements
Introduction
Part I. Basics: 1. The definition of the models
2. Measure on β
3. Witnessing quantifiers
4. The truth in N and the validity in K(F)
Part II. Second Order Structures: 5. Structures K(F,G)
Part III. AC0 World: 6. Theories IΔ0, IΔ0(R) and V10
7. Shallow Boolean decision tree model
8. Open comprehension and open induction
9. Comprehension and induction via quantifier elimination: a general reduction
10. Skolem functions, switching lemma, and the tree model
11. Quantifier elimination in K(Ftree,Gtree)
12. Witnessing, independence and definability in V10
Part IV. AC0(2) World: 13. Theory Q2V10
14. Algebraic model
15. Quantifier elimination and the interpretation of Q2
16. Witnessing and independence in Q2V10
Part V. Towards Proof Complexity: 17. Propositional proof systems
18. An approach to lengths-of-proofs lower bounds
19. PHP principle
Part VI. Proof Complexity of Fd and Fd(+): 20. A shallow PHP model
21. Model K(Fphp,Gphp) of V10
22. Algebraic PHP model?
Part VII. Polynomial-Time and Higher Worlds: 23. Relevant theories
24. Witnessing and conditional independence results
25. Pseudorandom sets and a Löwenheim–Skolem phenomenon
26. Sampling with oracles
Part VIII. Proof Complexity of EF and Beyond: 27. Fundamental problems in proof complexity
28. Theories for EF and stronger proof systems
29. Proof complexity generators: definitions and facts
30. Proof complexity generators: conjectures
31. The local witness model
Appendix. Non-standard models and the ultrapower construction
Standard notation, conventions and list of symbols
References
Name index
Subject index.

Dummy View - NOT TO BE DELETED