1
BOOLEAN RELATION
THEORY AND
INCOMPLETENESS
Harvey M. Friedman
Distinguished University Professor of Mathematics,
Philosophy, and Computer Science
The Ohio State University
June 13, 2011 version
TABLE OF CONTENTS
DEDICATION
ACKNOWLEDGEMENTS
PREFACE.
INTR
1
WHAT IS O-MINIMALITY?
by
Harvey M. Friedman
Ohio State University
November 8, 2006
We define the crucial notion of o-minimality for expansions
of the field of real numbers, in particularly friendly
purely mathematical terms. This should help bridge the
1
CONCEPT CALCULUS
APA PANEL on LOGIC IN PHILOSOPHY
by
Harvey M. Friedman
http:/www.math.ohio-state.edu/~friedman/
Distinguished University Professor of Mathematics,
Philosophy, and Computer Science
Ohio State University
Delivered December 28, 2007
Revise
1
WHAT IS O-MINIMALITY?
by
Harvey M. Friedman*
Ohio State University
[email protected]
http:/www.math.ohio-state.edu/%7Efriedman/
November 8, 2006
Revised September 6, 2007
Abstract. We characterize the o-minimal expansions of the
field of real
1
CONCEPT CALCULUS
APA PANEL on LOGIC IN PHILOSOPHY
by
Harvey M. Friedman
http:/www.math.ohio-state.edu/~friedman/
Distinguished University Professor of Mathematics,
Philosophy, and Computer Science
Ohio State University
Delivered December 28, 2007
Revise
1
DOES MATHEMATICS NEED NEW AXIOMS?
ASL Meeting, Urbana
Panel discussion: June 5, 2000
Harvey M. Friedman
The point of view of the set theory community is well
represented here. I want to concentrate on the perspective of
mathematicians outside set theory
1
WORKING WITH NONSTANDARD MODELS
Harvey M. Friedman
[email protected]
http:/www.mathpreprints.com/
July 31, 2003
Most of the research in foundations of mathematics that I
do in some way or another involves the use of nonstandard
models. I will
1
NEW BOREL INDEPENDENCE RESULTS
by
Harvey M. Friedman
April 30, 2007
May 7, 2007
sketch
1.
2.
3.
4.
5.
6.
Introduction.
Countable Borel equivalence relations on .
Countable Borel equivalence relations on 2.
Degrees into finitely generated groups.
Borel f
1
LECTURE NOTES ON BABY BOOLEAN RELATION THEORY*
Harvey M. Friedman
Department of Mathematics
Ohio State University
[email protected]
December 4, 2000
October 3, 2001
Abstract. This is an introduction to the most primitive form
of the new Boole
The number of certain integral polynomials and
nonrecursive sets of integers, part 2
Harvey M. Friedman
Department of Mathematics
Ohio State University
[email protected]
February 22, 2004
Abstract
We present some examples of mathematically natu
cfw_PAGE
THE AXIOMATIZATION OF SET THEORY BY EXTENSIONALITY,
SEPARATION, AND REDUCIBILITY
preliminary report
by
Harvey M. Friedman
Department of Mathematics
Ohio State University
Columbus, Ohio 43210
August 20, 1997
Revised October 28, 1997
[email protected]
BOOLEAN RELATION THEORY AND MORE
by
Harvey M. Friedman
Ohio State University
MIT LOGIC SEMINAR
November 3, 2009
[email protected]
www.math.ohio-state.edu/~friedman
4:30-6PM
We will start with the MORE.
We present the Unprovable Upper Shift Fixe
1
A WAY OUT
Harvey M. Friedman
Department of Mathematics
http:/www.math.ohio-state.edu/~friedman/
Ohio State University
August 28, 2002
ABSTRACT. We present a way out of Russells paradox for
sets in the form of a direct weakening of the usual
inconsistent
1
METAMATHEMATICS OF ULM THEORY
by
Harvey M. Friedman
Department of Mathematics
Ohio State University
http:/www.math.ohio-state.edu/~friedman/
June 24, 1999
November 25, 2001
INCOMPLETE DRAFT
Abstract. The classical Ulm theory provides a complete set of
i
1
A WAY OUT
Harvey M. Friedman
Ohio State University
August 28, 2002
ABSTRACT. We present a way out of Russells paradox for
sets in the form of a direct weakening of the usual
inconsistent full comprehension axiom scheme, which, with
no additional axioms,
1
This is an MS Word formatted version of my FOM posting #258
of November 27, 2005, at
http:/www.cs.nyu.edu/pipermail/fom/2005November/009395.html
Quite a number of typographical errors in the FOM posting
have been corrected.
P01 INCOMPLETENESS
by
Harvey
1
CONCEPT CALCULUS
by
Harvey M. Friedman
Mathematical Methods in Philosophy
Banff Research Center
University Professor
Ohio State University
February 21, 2007
1. THE GENERAL NATURE OF CONCEPT CALCULUS.
Concept Calculus is a new mathematical/philosophical
1
WHAT IS O-MINIMALITY?
by
Harvey M. Friedman*
Ohio State University
[email protected]
http:/www.math.ohio-state.edu/%7Efriedman/
November 8, 2006
Revised September 6, 2007
Revised October 29, 2007
Revised November 30, 2007
Abstract. We charact
1
COMPUTER ASSISTED CERTAINTY
by
Harvey M. Friedman
Computer Science Lecture Series
University of Kentucky
Ohio State University
January 25, 2007
ABSTRACT
Certainty (and the lack thereof) is a major issue in
mathematics and computer science. Mathematician
1
FINITE PHASE TRANSITIONS
Harvey M. Friedman*
Ohio State University
September 26, 2010
DRAFT
This topic has been discussed earlier on the FOM email list
in various guises. The common theme is: big numbers and
long sequences associated with mathematical o
1
WHAT YOU CANNOT PROVE 1: before 2000
by
Harvey M. Friedman
Department of Mathematics
Ohio State University
December 19, 2005
http:/www.math.ohio-state.edu/%7Efriedman/
Most of my intellectual efforts have focused around a
single general question in the
1
FINITE PHASE TRANSITIONS
Harvey M. Friedman*
Ohio State University
September 26, 2010
10AM
DRAFT
This topic has been discussed earlier on the FOM email list
in various guises. The common theme is: big numbers and
long sequences associated with mathemati
BOOLEAN RELATION
THEORY
by
Harvey M. Friedman
Distinguished University Professor
Mathematics, Philosophy, Computer
Science
Ohio State University
[email protected]
http:/www.math.ohio-state.edu/
~friedman/
University of Cambridge
Cambridge, Engl
1
FINITE PHASE TRANSITIONS
Harvey M. Friedman*
Ohio State University
September 25, 2010
DRAFT
This topic has been discussed earlier on the FOM email list
in various guises. The common theme is: big numbers and
long sequences associated with mathematical o
BOOLEAN RELATION
THEORY
by
Harvey M. Friedman
Ohio State University
[email protected]
http:/www.math.ohio-state.edu/%7Efriedman/
Mathematical Logic Seminar
Carnegie Mellon University
March 27, 2009
BABY BRT
BRT is always based on a choice of BR
1
ADJACENT RAMSEY THEORY
by
Harvey M. Friedman*
Department of Mathematics
Ohio State University
January 23, 2008
July 27, 2010
August 29, 2010
DRAFT
Abstract. We introduce Adjacent Ramsey Theory, which
investigates solutions to the shift equation f(x1,.,x
1
SELECTION FOR BOREL RELATIONS
by
Harvey M. Friedman*
Department of Mathematics
Ohio State University
[email protected]
http:/www.math.ohio-state.edu/~friedman/
September 30, 2001
Abstract. We present several selection theorems for Borel
relat
1
The manuscript below corresponds to my talk presented to
the mathematics Colloquium, but with references added
later. The references are by no means complete,
particularly with regard to books that I could not
conveniently locate. I want to thank Dan Bu
1
BOREL AND BAIRE REDUCIBILITY
by
Harvey M. Friedman
Department of Mathematics
Ohio State University
Columbus, Ohio 43210
[email protected]
http:/www.math.ohio-state.edu/~friedman/
May 25, 1999
September 2, 1999
INTRODUCTION
The Borel reducibil
1
ON EXPANSIONS OF O-MINIMAL STRUCTURES
PRELIMINARY REPORT
by
Harvey M. Friedman
Department of Mathematics
Ohio State University
November 23, 1996
[email protected]
www.math.ohio-state.edu/~friedman/
An o-minimal structure is any relational str