[FOM] BRT book

[Harvey Friedman]

PARTIAL BOOK ANNOUNCEMENT

Harvey M. Friedman
September 15, 2004

BOOLEAN RELATION THEORY

TABLE OF CONTENTS

Chapter 1. Introduction to BRT.
{partial 10 page draft exists)

1.1. General Formulation.
1.2. BRT Settings.
1.3. EBRT and the Complementation Theorem.
1.4. IBRT and the Thin Set Theorem.

Chapter 2. Classifications.
{partial 40 page draft exists, complete for 4.3.}

2.1. Methodology.
2.2. EBRT, IBRT in A,fA.
3.3. EBRT, IBRT in A,fA,fN.
4.3. EBRT in A,B,fA,fB.

Chapter 3. 6561 cases in A,B,C,fA,fB,fC,gA,gB,gC.
{complete 118 page draft exists}

3.1. Prelimiinaries.
3.2. Three Useful Lemmas.
3.3. Single Clauses (duplicates).
3.4. AAAA.
3.5. AAAB.
3.6. AABA.
3.7. AABB.
3.8. AABC.
3.9. ABBA.
3.10. ABAB.
3.11. ABBC.
3.12. ABAC.
3.13. ACBC.
3.14. Annotated Tables.
3.15. Some Facts. 

Chapter 4. Proof of Exotic Case.
{24 page draft exists, complete for 4.1, 4.2.}

4.1. Mahlo Cardinals of Finite Order.
4.2. Proof using Mahlo Cardinals.
4.3. Proof using 1-consistency.

Chapter 5. Independence of Exotic Case.
{132 page draft exists, complete for 5.1-5.10.}

5.1. Propositions C,D and Length 3 Towers.
5.2. From Length 3 Towers to Length n Towers.
5.3. Countable Nonstandard Models with Limited Indiscernibles.
5.4. Limited Formulas, Limited Indiscernibles, x-definability, Normal Form.
5.5. Comprehension, Indiscernibles.
5.6. Pi01 Correct Internal Arithmetic, Simplification.
5.7. Transfinite Induction, Comprehension, Indiscernibles, Infinity, Pi01
Correctness. 
5.8. ZFC + V = L, Indiscernibles, and Pi01 Correct Arithmetic.
5.9. ZFC + V = L + {(therexists kappa)(kappa is k-Mahlo)}_k + TR(Pi01).
5.10. Equivalence with 1-consistency.
5.11. Further Results.
 
Chapter 6. The Future.
{No draft exists}
 
Total of 324 pages of partial draft text exists in MS Word, 12 pt. font.

Expected submission date: Jan 1, 2005.

Harvey M. Friedman