BOOLEAN RELATION THEORY BOOK

BOOLEAN RELATION THEORY AND INCOMPLETENESS will appear in the Lecture Notes in Logic Series of the Association for Symbolic Logic, in conjunction with Cambridge University Press.

DEDICATION. 4/20/11. 1 page.   0.DEDICATION042011

ACKNOWLEDGEMENTS. 4/21/11. 2 pages.   0.Acknow042111

PREFACE.  5/5/11. 4 pages.  1Preface050511

INTRODUCTION.  CONCRETE MATHEMATICAL INCOMPLETENESS. 6/13/11. 237 pages. “What’s new?” will be added.  0.Intro061311

CHAPTER 1. INTRODUCTION TO BRT.
1.1. General Formulation. 2/6/11. 21 pages.  1.1GenForm020611
1.2. Some BRT Settings. 2/6/11. 8 pages.  1.2SomeBRTSet020611
1.3. Complementation Theorems. 7/11/10. 17 pages.  1.3Comp071110
1.4. Thin Set Theorems. 2/7/11. 20 pages.  1.4ThinSet020711

CHAPTER 2. CLASSIFICATIONS.
2.1. Methodology. 2/9/11. 14 pages.  2.1.Meth020911
2.2. EBRT, IBRT in A,fA. 7/11/10. 9 pages.  2.2.A,fA071110
2.3. EBRT, IBRT in A,fA,fU. 11/1/10. 22 pages.  2.3.A,fA,fU110110
2.4. EBRT in A,B,fA,fB,inclusion on (SD,INF). 6/23/10. 15 pages.  2.4.A,B,fA,fBSD062310
2.5. EBRT in A,B,fA,fB,inclusion on (ELG,INF). 11/01/10. 22 pages.  2.5.A,B,fA,fBELG110110
2.6. EBRT in A1,…,Ak,fA1,…,fAk,inclusion on (MF,INF). 6/23/10. 2 pages.  2.6.A1-AkfA1-fAkMF062310
2.7. IBRT in A1,…,Ak,fA1,…,fAk,inclusion on (SD,INF), (ELG,INF), (MF,INF). 3/11/09. 13 pages.  2.7IBRTA1-Ak102508

CHAPTER 3. 6561 CASES OF EQUATIONAL BOOLEAN RELATION THEORY.
3.1. Preliminaries. 2/17/11. 30 pages.  3.1Prel021711
3.2. Some Useful Lemmas. 3/1/09. 6 pages.  3.2Useful030109
3.3. Single Clauses (duplicates). 3/1/09. 5 pages.  3.3Single030409
3.4. AAAA. 3/1/09. 3 pages.  3.4AAAA030109
3.5. AAAB. 3/1/09. 5 pages.  3.5AAAB030109
3.6. AABA. 3/1/09. 10 pages.   3.6AABA030109
3.7. AABB. 3/1/09. 3 pages.  3.7AABB030109
3.8. AABC. 3/1/09. 13 pages.  3.8AABC030109
3.9. ABAB. 3/1/09. 4 pages.  3.9ABAB030109
3.10. ABAC. 3/1/09. 4 pages.  3.10ABAC030109
3.11. ABBA. 3/4/09. 3 pages.   3.11ABBA030409
3.12. ABBC. 3/1/09. 14 pages.  3.12ABBC030109
3.13. ACBC. 3/1/09. 6 pages.  3.13ACBC030109
3.14. Annotated Table of Representatives. 3/1/09. 26 pages.  3.14tables030109
3.15. Some Observations. 2/18/11. 4 pages.  3.15observ021811

CHAPTER 4. PROOF OF EXOTIC CASE.
4.1. Strongly Mahlo Cardinals of Finite Order. 7/13/10. 9 pages.   4.1Mahlo071310
4.2. Proof using Strongly Mahlo Cardinals. 7/11/10. 23 pages.  4.2Proof071110
4.3. Some Existential Sentences. 7/11/10. 11 pages.  4.3exist071110
4.4. Proof using 1-consistency. 7/11/10. 13 pages.  4.4use1-Con071110

CHAPTER 5. INDEPENDENCE OF EXOTIC CASE.
5.1. Propositions C,D and Length 3 Towers. 1/9/11. 9 pages.  5.1.PropC,D010911
5.2. From Length 3 Towers to Length n Towers. 1/9/11. 18 pages.  5.2Leng3tow010911
5.3. Countable Nonstandard Models with Limited Indiscernibles. 1/9/11. 26 pages.  5.3CntbleNon010911
5.4. Limited Formulas, Limited Indiscernibles, x-definability, Normal Form. 1/9/11. 15 pages.  5.4limForm010911
5.5. Comprehension, Indiscernibles. 1/9/11. 9 pages.  5.5comp010911
5.6. Pi01 Correct Internal Arithmetic, Simplification. 1/9/11. 21 pages.  5.6Pi01cor010911
5.7. Transfinite Induction, Comprehension, Indiscernibles, Infinity, Pi01 Correctness. 1/9/11. 27 pages.  5.7Transf010911
5.8. ZFC + V = L, Indiscernibles, and Pi01 Correct Arithmetic. 1/9/11. 29 pages.  5.8ZFC010911
5.9. ZFC + V = L + {(therexists kappa)(kappa is strongly k-Mahlo)}_k + TR(Pi01,L), and 1-Con(SMAH). 1/10/11. 14 pages.  5.9ZFCL011011

CHAPTER 6. FURTHER RESULTS.

6.1. Propositions D-H. 07/13/10. 18 pages.  6.1Further071310
6.2. Effectivity. 07/27/10. 27 pages.  6.2.Effect072710
6.3. A Refutation. 07/14/10. 4 pages  6.3Refute071410

REFERENCES. 6/13/11. 26 pages.  7References061311

APPENDIX A. 07/11/10. 4 pages.  0AppA071110

APPENDIX B. 7/27/10. By Francoise Point. On the Expansion (N;+;2^x) of Presburger Arithmetic. 15 pages.  0AppB072710

INDEX. 11/21/09. 12 pages. Will be redone.  0.Index112109

ENTIRE BOOK, SINGLE FILE. BOOLEAN RELATION THEORY AND INCOMPLETENESS . 6/13/11 version. 819 pages without Appendix B, by Francoise Point, without Index, and without “what’s new?”. Index, and “What’s new” will be added in page proofs, needs to be added.  0EntireBook061311