BOOLEAN RELATION THEORY BOOK

9/2/17 – The current plan is to combine BOOLEAN RELATION THEORY AND INCOMPLETENESS below with all of my results over the years on Incompleteness, particularly including new developments called Emulation Theory, into a larger book called CONCRETE MATHEMATICAL INCOMPLETENESS.

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