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1. Preprints, Drafts, and Abstracts
- The Reverse Mathematics program originated with the publications 'Some Systems of Second Order Arithmeitc aand Their Use, Proceedings of the 1974 International Congress of Mathematicians, Vol. 1, (1975), pp. 235-242', and 'Subsystems of Second Order Arithmetic with Restricted Induction I,II, abstracts, J. of Symbolic Logic, Vol. 41, No. 2 (1976), pp. 557-559, as well as the following widely distributed unpublished manuscripts.
'The Analysis Of Mathematical Texts, And Their Calibration In Terms Of Intrinsic Strength I', April 3, 1975, 7 pages. 'The Analysis Of Mathematical Texts, And Their Calibration In Terms Of Intrinsic Strength II', April 8, 1975, 5 pages. 'The Analysis Of Mathematical Texts, And Their Calibration In Terms Of Intrinsic Strength III ', May 19, 1975, 26 pages. 'The Analysis Of Mathematical Texts, And Their Calibration In Terms Of Intrinsic Strength IV', August 15, 1975, 32 pages. 'The Logical Strength Of Mathematical Statements', October 15, 1975, 1 page. 'The Logical Strength Of Mathematical Statements I', August, 1976, 20 pages. See also: (with S. Simpson), Issues and Problems in Reverse Mathematics, in: Computability Theory and its Applications, Contemporary Mathematics, volume 257, 2000, 127-144.
  `Combinatorial
set theoretic statements of great logical strength', 1995, 4 pages,
abstract.
-
  `Some
Decision Problems Related to Hilbert's Tenth Problem', January 15,
1996, 2 pages, abstract.
-
  `Extremely
large cardinals in the rationals', August 1996, 4 pages, abstract.
-
  `Countable
model theory and large cardinals', September 1996, 3 pages, abstract.
-
  `On
Expansions of o-Minimal Structures', November 23, 1996, 4 pages, draft.
-
  `The
Formalization of Mathematics', May 21, 1997, 11 pages, draft.
-
  `Some
Historical Perspectives on Certain Incompleteness Phenomena', May 21,
1997, 5 pages, draft.
-
  `Transfer
Principles in Set Theory', May 21, 1997, 44 pages, draft.
-
  'The
interpretation of set theory in pure predication theory', August 20,
1997, 64 pages, draft.
-
  `Applications
of Large Cardinals to Graph Theory', October 23, 1997, 36 pages, draft.
-
  `The
interpretation of set theory in mathematical predication theory', October
25, 1997, 10 pages, draft.
-
  `The
axiomatization of set theory by extensionality, separation, and reducibility',
October 28, 1997, 71 pages, draft.
-
  `Applications
of Large Cardinals to Borel Functions', November 26, 1997, 3 pages,
abstract.
-
  `Finite
Trees and the Necessary Use of Large Cardinals', March 22, 1998, 58
pages, draft.
-
  `'Subtle
Cardinals and Linear Orderings', April 1998, 52 pages, See Publications.
-
  'Long
Finite Sequences', October 8, 1998, 50 pages. See Publications.
  'Interpretability
and Definability in Expansions,' with Chris Miller, November,
1998, 5 pages, abstract.
-
  'Some
Decision Problems of Enormous Complexity', May 6, 1999, 10 pages, See Publications.
-
  `A
Consistency Proof for Elementary Algebra and Geometry', August 23,
1999, 38 pages, draft.
`Borel and Baire reducibility', September 2, 1999, 11 pages. See Publications.
-
  `Conservation',
September 24, 1999, 7 pages, draft.
-
  `Adjacent
Ramsey Theory', October 2, 1999, 3 pages, draft.
-
  `Quadratic
Axioms', January 3, 2000, 9 pages, draft.
-
  `Geometry
Axioms', January 8, 2000, 4 pages, draft.
-
  `Completeness
of Intuitionistic Propositional Calculus', March 20, 2000, 5 pages,
draft.
`The Ackermann function in elementary algebraic geometry', October 21, 2000, 18 pages, draft.
`Selection for Borel relations', September 20, 2001, 24 pages. See Publications.
`Boolean relation theory notes', October 6, 2001, 20 pages, draft.
`Metamathematics of comparability', October 7, 2001, 24 pages. See Publications.
`Finite reverse mathematics', October 19, 2001, 28 pages, draft.
`Maximal nonfinitely generated subalgebras', October 19, 2001, 16 pages. See Publications.
`Metamathematics of Ulm theory', November 25, 2001, 33 pages, draft.
`Primitive independence results', July 13, 2002, 23 pages. See Publications.
`Three quantifier sentences', July 14, 2002, 33 pages. See Publications.
-
`A Way Out', August 28, 2002, 49 pages. See Publications.
-
`Equational Boolean relation theory', September 3, 2002, 25 pages, draft.
-
`Philosophical Problems in Logic', Seminar notes at the Princeton Philosophy Department, September-December, 2002, 107 pages.
-
`Philosophy of Mathematics', Seminar notes at the Princeton Philosophy Department, September-December, 2002, 71 pages.
`Sentential Reflection', January 5, 2003, 3 pages, draft.
`Restrictions and extensions', February 17, 2003, 3 pages, draft.
`Elemental sentential reflection', March 3, 2003, 6 pages, draft.
`Similar subclasses', March 11, 2003, 3 pages, draft.
`Working with Nonstandard Models', July 31, 2003, 24 pages. See Publications.
`The number of certain integral polynomials and nonrecursive sets of integers, part 2', February 22, 2004, 13 pages. See Publications.
`Strict reverse mathematics', January 31, 2005, 24 pages, draft.
'Relational system theory', May 26, 2005, 12 pages, abstract.
'The inevitability of logical strength', May 31, 2005, 13 pages, draft.
'Pi01 Incompleteness: finite set equations', December 9, 2005, 6 pages, abstract. This supercedes the previous 11/30/05, 12/3/05, 12/4/05 abstracts.
-
'Pi01 Incompleteness: finite graph theory 1', January 30, 2006, 4 pages, abstract.
-
'Pi01, Pi00 Incompleteness: finite graph theory', February 25, 2006, 4 pages, abstract.
-
(with J. Avigad), Combining decision procedures for the reals, 42 pages. See Publications.
-
'Concept Calculus', October 25, 2006, 42 pages, abstract. Supercedes August 7, 2006 version.
-
'Exotic Prefix Theory', September 14, 2006, 7 pages, abstract. Supercedes earlier version.
-
'What is o-minimality?', November 30, 2007, 19 pages, Supercedes earlier versions. See Publications.
-
'Formal statements of Goedel's second incompleteness theorem', January 14, 2007, 8 pages, abstract.
-
'New Borel Independence Results', May 7, 2007, 20 pages. Many proofs sketched.
-
'My Forty Years On His Shoulders', October 31, 2009, to appear in the proceedings of the Goedel Centenary meeting in Vienna, held in April, 2006, Horizons of Truth, 69 pages. Supercedes earlier versions.
-
'The Inevitability of Logical Strength: strict reverse mathematics', 65 pages. See Publications.
- The Nineteenth Annual Tarski Lectures. Interpretations of Set Theory in Discrete Mathematics and Informal Thinking. Delivered April 9,11,13, 2007 at the University of California at Berkeley. Manuscripts based on these lectures: 1. Interpretations, According to Tarski, May 24, 2007, 42 pages. Many proofs sketched.
2. Interpreting Set Theory in Discrete Mathematics: Boolean Relation Theory, May 24, 2007, 15 pages. Abstract. 3. Interpreting Set Theory in Ordinary Thinking: Concept Calculus, 12 pages. Abstract. 
-
(with S. Kieffer, J. Avigad), A language for mathematical knowledge management, 16 pages, August, 2008. To appear in speical issue of Studies in Logic, Grammar and Rhetoric, 2008. http://www.andrew.cmu.edu/user/avigad/Papers/mkm/index.html See Publications.
-
Limitations on our Understanding of the Behavior of Simplified Physical Systems, Proceedgins of the 2007 San Marino Symposium on "Science Reason and Truth"; Ed. by M. Bersanelli, C. Harper and P. Van Inwagen, Univer. of Notre Dame Press, to appear. See Publications.
Concept Calculus: Much Better Than, October 31, 2009, 48 pages. To appear in New Frontiers in Research on Infinity, ed. Michael Heller and W. Hugh Woodin, Cambridge University Press, 2010. (Initial paper on Concept Calculus). See Publications.
Boolean Relation Theory and More. This is actually a sketchy treatment of The Upper Shift Fixed Point Theorem, given at the MIT Logic Seminar, November 3, 2009. 10 pages.
-
Decision Problems in Euclidean Geometry. This is an advanced draft nearing completion for publication. August 29, 2010, 33 pages. This version (supercedes August 23, 2010 version) is based on Integral Domains of Characteristic Zero, and Ordered Rings.
-
Adjacent Ramsey Theory. Draft. Key proofs are given. August 29, 2010, 17 pages.
Kernel Structure Theory. Abstract. Independent Pi01 sentences. August 29, 2010, 8 pages.
Equational Representations.This is an advanced draft nearing completion for publication. September 23, 2010. 17 pages.
Finite Phase Transitions. Draft. September 26, 2010. 9 pages. NOTE: This manuscript initiates a new line of research on phase transitions, but Royce Peng has pointed out that it has errors in detail. He is in communication concerning stronger claims.
The Upper Shift Kernel Theorems. Draft. October 9, 2010. 7 pages. Supersedes earlier versions.
-
Invariant Maximal Cliques and Incompleteness, October 7, 2011 version, 132 pages. Supersedes original October 4, 2011, and October 6, 2011 versions. Corrected several inaccurate statements, improved exposition. Submitted for publication.
2. Lecture Notes
`Invited Talks, January, 1997 to April 2, 2012, 21 pages.
-
  `The
Formalization of Mathematics', February, 1997, 11 pages.
-
  `Ramsey
Theory and Enormous Lower Bounds', April 5, 1997, 11 pages.
`Transfer
Principles in Set Theory', May 7, 1997, 21 pages.
-
  `Axiomatization
of Set Theory by Extensionality, Separation, and Reducibility', October
5, 1997, 12 pages.
-
  `From
Russell's Paradox to Higher Set Theory', October 10, 1997, 13 pages.
-
  `Finite
Trees and the Necessary Use of Large Cardinals', January 10, 1998,
8 pages.
-
  `Unprovable
Theorems in Discrete Mathematics', April 26, 1999, 10 pages.
-
  `A
Theory of Strong Indiscernibles', April 28, 1999, 2 pages.
-
  `A
Complete Theory of Everything: satisfiability in the universal domain',
October 10, 1999, 15 pages.
-
  `Decreasing
Chains of Algebraic Sets', November 12, 1999, 12 pages.
-
  `Discrete
Independence Results', November 16, 1999, 13 pages.
-
  `The
Mathematical Meaning of Mathematical Logic', April 21, 2000, 14 pages.
-
  `Does
Mathematics Need New Axioms?', May 30, 2000, 13 pages.
-
  `A
Logician Looks at Programming', May 31, 2000, 4 pages.
-
  `Foundations
of Mathematics: past, present, and future', May 31, 2000, 8 pages.
-
  `Enormous
Integers in Real Life', June 1, 2000, 11 pages.
-
  `New
Axioms Panel', June 5, 2000, 8 pages.
`Lecture notes on baby Boolean relation theory', October 3, 2001, 11 pages.
`Does normal mathematics need new axioms?', October 26, 2001, 12 pages.
`Lecture notes on term rewriting and computational complexity', November 7, 2001, 12 pages.
`Lecture notes on enormous integers', November 22, 2001, 11 pages.
`Issues in the foundations of mathematics', Godel Lecture, Association for Symbolic Logic, June 2, 2002, 14 pages.
`Demonstrably necessary uses of abstraction', Hans Rademacher Lectures, University of Pennsylvania, September 17-20, 2002, 53 pages.
`Adventures in the foundations of mathematics', VIGRE Lectures, Ohio State University, April 28-May 7, 2003, 64 pages.
`Unprovable theorems', April 19, 2005, 11 pages.
-
`Clay Millenium Problem: P = NP', Mathematics Colloquium, Ohio State University, October 20, 2005, 19 pages.
-
'What you cannot prove 1: before 2000', December 19, 2005, 18 pages.
-
'Forty years on his shoulders', Goedel Centenary, April 25, 2006, 9 pages.
-
'Remarks on Goedel Phenomena and the field of reals', Goedel Centenary, April 27, 2006, 6 pages.
-
'Remarks on the unknowable', Goedel Centenary, April 28, 2006, 6 pages.
-
'Adventures in the Verification of Mathematics', Computer Science Colloquium, Ohio State University, June 8, 2006, 19 pages.
-
'Search for Consequences', Logic Colloquium '06, August 9, 2006, Nijmegen, Netherlands, 15 pages.
-
'Goedel's Legacy in Mathematical Philosophy', Logic Colloquium '06', August 9, 2006, Nijmegen, Netherlands, 6 pages.
-
'Contemporary perspectives on Hilbert's second problem and the Goedel incompleteness theorems', AMS panel, New Orleans, January 6, 2007, 7 pages.
-
'Computer assisted certainty', Computer Science Lecture Series, University of Kentucky, January 25, 2007, 17 pages.
-
'Concept Calculus', Mathematical Methods in Philosophy, Banff, Canada, February 21, 2007, 9 pages.
-
'Limitations on our understanding of the behavior of simplified physical systems', Science, Reason, and Truth, San Marino, August 17-19, 2007, 26 pages.
-
'Concept Calculus', APA Panel on Logic in Philosophy, APA Eastern Division Annual Meeting, Baltimore Maryland, January 2, 2008, 17 pages. Supercedes 1/1/2008 and earlier versions.
-
'LOGIC: Interdisciplinary Adventures in Mathematics, Philosophy, Computer Science, and Education', University Distinguished Lecture, The Ohio State University, April 23, 2008, 16 pages. Streaming video at http://www.osu.edu/facultystaff/university_awards/2007/lecturer.php
-
Concept Calculus, Carnegie Mellon University, March 26, 2009, Pure and Applied Logic Colloquium.
-
Boolean Relation Theory, Carnegie Mellon University, March 27, 2009, Mathematical Logic Seminar.
-
Decision Problems in Strings and Formal Methods, Carnegie Mellon University, Theory/POP Seminar, March 27, 2009.
-
Foundational Adventures for the Future, Honoree Lecture at the Foundational Adventures Conference in honor of Harvey Friedman's 60th Birthday, Columbus Ohio, May 14-17, 2009. Lecture devlivered May 15, 2009.
-
Concept Calculus, Department of Philosophy, MIT, November 4, 2009, 22 pages.
-
Decision Procedures for Verification, Joint Theory of Computation and Programming Language Seminar, Computer Science, Harvard University, October 9, 2009, 28 pages. Also delivered at the MIT Computer Science Department, November 4, 2009.
-
Strict Reverse Mathematics, Reverse Mathematics Workshop, University of Chicago, November 7, 2009, 19 pages.
-
Unprovable Theorems, Mathematics/Philosophy talk at Harvard University, October 8, 2009. Also delivered at the Boston Mathematics Colloquium, MIT, November 5, 2009. 30 pages.
Shocking(?) Unprovability, Lecture at the Mathematics Department of The Ohio State University, April 16, 2010. 20 pages.
-
Aspects of Constructive Set Thoery and Beyond, Amerterdam Conference on Set Theory, Classical and Constructive, 1 hour, May 6, 2010, 20 pages.
Concrete Incompleteness from EFA Through Large Cardinals, May 10, 2010, Institute for Logic, Language, and Computation, University of Amsterdam, 2 hours. 31 pages.
-
Concrete Mathematical Incompleteness, University of Cambridge, UK, November 8, 2010. Minor revisions November 18, 2010. 28 pages.
-
Boolean Relation Theory, University of Cambridge, UK, November 10, 2010. Minor revisions November 18, 2010. 38 pages.
- Adventures In Logic For Undergraduates. Lecture Series. 5 Lectures, Ohio State University. Lecture 1: Logical Connectives, January 18, 2011
Lecture 2: Logical Quantifiers, January 25, 2011 Lecture 3: Turing Machines, February 1, 2011 Lecture 4: Goedel's Blessing and Goedel's Curse, February 8, 2011 Lecture 5: Foundations of Mathematics, February 15, 2011 
-
Past, Present, and Future Directions in the Foundations of Mathematics. Trends in Logic, Kurt Goedel Society, Vienna Academy of Sciences, Vienna, Austria, April 29, 2011, 1 hour. 37 pages.
-
An Appreciation of Hilary's Mathematical Work, delivered June 1, 2011 at Philosophy in an Age of Science, Conference in Honor of Hilary Putnam's 85th Birthday. 45 minutes. Revised June 7, 2011. 14 pages.
-
Maximality and Incompleteness, deelivered March 1, 2012, at the Brandeis-Harvard-MIT-Northeastern Joint Mathematics Colloquium, at Harvard. 1 hour. Revised March 5, 2012. 31 pages.
-
Are the Usual Axioms Sufficient?, delivered March 10, 2012 at Patrick Suppes' 90th Birthday Celebration, at Stanford. 20 minutes. 15 pages.
-
Goedel's Second Theorem: Its Meaning and Use, delivered March 17, 2012 at AMS Special Session, on The Legacy of Goedel's Second Incompleteness Theorem for the Foundations of Mathematics, Washington DC, 45 minutes. 30 pages.
-
Incompleteness 1, Invitation to Mathematics Series, Department of Mathematics, Ohio State University, April 25, 2012. 20 pages.
-
Incompleteness 1I, Invitation to Mathematics Series, Department of Mathematics, Ohio State University, May 2, 2012. 21 pages.
3. Book Drafts
Expect that the various sections will be updated from time to time.
BOOLEAN RELATION THEORY AND INCOMPLETENESS
DEDICATION. 4/20/11. 1 page.
ACKNOWLEDGEMENTS.
4/21/11. 2 pages.
PREFACE. 7/27/10. 5/5/11. 4 pages.
INTRODUCTION. CONCRETE MATHEMATICAL INCOMPLETENESS. 6/13/11. 237 pages. "What's new?" deleted from 0.14. Will be added in page proofs, within 3 months.
CHAPTER 1. INTRODUCTION TO BRT.
1.1. General Formulation. 2/6/11. 21 pages.
1.2.
Some BRT Settings. 2/6/11. 8 pages.
1.3. Complementation Theorems. 7/11/10. 17 pages.
1.4. Thin Set Theorems. 2/7/11. 20 pages.
CHAPTER 2. CLASSIFICATIONS.
2.1. Methodology. 2/9/11. 14 pages.
2.2. EBRT, IBRT in A,fA. 7/11/10. 9 pages.
2.3. EBRT, IBRT in A,fA,fU. 11/1/10. 22 pages.
2.4. EBRT in A,B,fA,fB,inclusion on (SD,INF). 6/23/10. 15 pages.
2.5. EBRT in A,B,fA,fB,inclusion on (ELG,INF). 11/01/10. 22 pages.
2.6. EBRT in A1,...,Ak,fA1,...,fAk,inclusion on (MF,INF). 6/23/10. 2 pages.
2.7. IBRT in A1,...,Ak,fA1,...,fAk,inclusion on (SD,INF), (ELG,INF), (MF,INF). 3/11/09. 13 pages.
CHAPTER 3. 6561 CASES OF EQUATIONAL BOOLEAN RELATION THEORY.
3.1. Preliminaries. 2/17/11. 30 pages.
3.2. Some Useful Lemmas. 3/11/09. 6 pages.
3.3. Single Clauses (duplicates). 3/11/09. 5 pages.
3.4. AAAA. 3/11/09. 3 pages.
3.5. AAAB. 3/11/09. 5 pages.
3.6. AABA. 3/11/09. 10 pages.
3.7. AABB. 3/11/09. 3 pages.
3.8. AABC. 3/11/09. 13 pages.
3.9. ABAB. 3/11/09. 4 pages.
3.10. ABAC. 3/11/09. 4 pages.
3.11. ABBA. 3/11/09. 3 pages.
3.12. ABBC. 3/11/09. 14 pages.
3.13. ACBC. 3/11/09. 6 pages.
3.14. Annotated Table of Representatives. 3/11/09. 26 pages.
3.15. Some Observations. 3/11/09. 4 pages.
CHAPTER 4. PROOF OF EXOTIC CASE.
4.1. Strongly Mahlo Cardinals of Finite Order. 7/13/10. 9 pages.
4.2. Proof using Strongly Mahlo Cardinals. 7/11/10. 23 pages.
4.3. Some Existential Sentences. 7/11/10. 11 pages.
4.4. Proof using 1-consistency. 7/11/10. 13 pages.
CHAPTER 5. INDEPENDENCE OF EXOTIC CASE.
5.1. Propositions C,D and Length 3 Towers. 1/9/11. 9 pages.
5.2. From Length 3 Towers to Length n Towers. 1/9/11. 18 pages.
5.3. Countable Nonstandard Models with Limited Indiscernibles. 1/9/11. 26 pages.
5.4. Limited Formulas, Limited Indiscernibles, x-definability, Normal Form. 1/9/11. 15 pages.
5.5. Comprehension, Indiscernibles. 1/9/11. 9 pages.
5.6. Pi01 Correct Internal Arithmetic, Simplification. 1/9/11. 21 pages.
5.7. Transfinite Induction, Comprehension, Indiscernibles, Infinity, Pi01 Correctness. 1/9/11. 27 pages.
5.8. ZFC + V = L, Indiscernibles, and Pi01 Correct Arithmetic. 1/9/11. 29 pages.
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.
CHAPTER 6. FURTHER RESULTS.
6.1. Propositions D-H. 07/13/10. 18 pages.
6.2. Effectivity. 07/27/10. 27 pages.
6.3. A Refutation. 07/14/10. 4 pages
REFERENCES. 6/13/11. 26 pages.
APPENDIX A. 07/11/10. 4 pages.
APPENDIX B. 7/27/10. By Francoise Point. On the Expansion (N;+;2^x) of Presburger Arithmetic.
15 pages.
INDEX. 03/11/09. 12 pages. Will be redone.
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, within 3 months.
4. FOM e-mail List
The FOM e-mail list is an automated e-mail list devoted to lively discussion
of the foundations of mathematics. As of June 13, 2011, there are 1218 entries on the subscription list at http://www.cs.nyu.edu/mailman/roster/fom.
The FOM began as an unautomated e-mail list that I set up, in 1997, with about a couple of dozen scholars in foundations of mathematics. The initial discussions were very lively, and mostly concerned criticisms and defenses of my strong views on the speical status of foundations of mathematics within mathematical logic. Several highly respected model theorists engaged in the traffic of the e-mail list.
Later in 1997, Steve Simpson brought technology to bear and converted the operation to an automated e-mail list using the program Majordomo. Steve served in the capacity of moderator until 2002. In those early years, we both actively contributed to, and aggressively promoted, the FOM. After stepping down as moderator, Steve remained on the FOM Editorial Board in a largely honorarial capacity. Martin Davis took over as moderator till this day.
From the beginning, I have been the principal contributor of state of the art mathematical material, having posted 467 detailed abstracts in foundations of mathematics - numbered and indexed for convenient retrieval (as of June 13, 2011). I have also authored some hundreds of less formal exchanges about a variety of topics in foundations of mathematics.
I use it as my major method of dissemination of new mathematical results and ideas, and frequently obtain valuable feedback from unexpected sources. I do not know of any other scholars in the foundations of mathematics who actively or regularly use this method of dissemination, but it is being systematically used by several prominent mathematicians, including Timothy Gowers and Terence Tao.
Information about the FOM e-mail list can be obtained at http://www.cs.nyu.edu/mailman/listinfo/fom
The FOM archives are located at http://www.cs.nyu.edu/pipermail/fom. Postings to the FOM e-mail list can be conveniently retrieved from there.
[Degrees and Employment History] [Distinctions]
[Publications] [Others about Friedman]
[Downloadable Manuscripts] [Comments and Ideas]
[Adventures in Music]
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