Friedman, Harvey - Department of Mathematics, Ohio State University

• THE AXIOMATIZATION OF SET THEORY BY EXTENSIONALITY, SEPARATION, AND REDUCIBILITY
• LONG FINITE SEQUENCES Harvey M. Friedman*
• BOOLEAN RELATION THEORY NOTES Harvey M. Friedman*
• DECISION PROCEDURES FOR VERIFICATION
• ACKNOWLEDGEMENTS I have interacted with many scholars over the years
• SHOCKING(?) UNPROVABILITY
• FINITE PHASE TRANSITIONS Harvey M. Friedman*
• R(x1,...,xk) (k,n,m,R1,...,Rn-1)
• APPLICATIONS OF LARGE CARDINALS TO GRAPH THEORY
• SUBTLE CARDINALS AND LINEAR Harvey M. Friedman
• Some Decision Problems of Enormous Complexity Harvey M. Friedman
• Harvey M. Friedman Ohio State University
• 2.3. EBRT, IBRT in A,fA,fU. We redo section 2.2 for the signature A,fA,fU, with the
• CONCEPT CALCULUS: MUCH BETTER Harvey M. Friedman*
• LIMITATIONS ON OUR UNDERSTANDING OF THE BEHAVIOR OF SIMPLIFIED PHYSICAL SYSTEMS
• ADVENTURES IN THE VERIFICATION OF MATHEMATICS Harvey M. Friedman
• THE FORMALIZATION OF MATHEMATICS Harvey M. Friedman
• FINITE TREES AND THE NECESSARY USE OF LARGE CARDINALS
• LOGIC: Interdisciplinary Adventures in Mathematics, Philosophy, Computer
• PRINCIPAL CLASSES OF FUNCTIONS AND SETS
• THE INTERPRETATION OF SET THEORY IN PURE PREDICATION THEORY preliminary report
• Logical Methods in Computer Science Vol. 2 (4:4) 2006, pp. 142
• A THEORY OF STRONG INDISCERNIBLES Harvey M. Friedman
• The standard axiomatization of mathematics is given by the formal system ZFC, which is read "Zermelo Frankel set
• BOOLEAN RELATION Harvey M. Friedman
• BOOLEAN RELATION INCOMPLETENESS
• 5.4. Limited formulas, limited indiscernibles, x-definability, normal form.
• NEW BOREL INDEPENDENCE RESULTS Harvey M. Friedman
• THE INEVITABILITY OF LOGICAL STRENGTH Harvey M. Friedman
• 5.5. Comprehension, indiscernibles. We fix M = (A,<,0,1,+,-,,,log,E,c1,c2,...) and terms
• EXOTIC PREFIX THEORY Harvey M. Friedman
• 4.4. Proof using 1-consistency. In this section we show that Propositions A,B can be proved
• SOME HISTORICAL PER SPECTIVES ON CERTAIN INCOMPLETENESS Harvey M. Friedman
• University of Pennsylvania Department of Mathematics
• 4.2. Proof using Strongly Mahlo Cardinals. Recall Proposition A from the beginning of section 3.1.
• WHAT IS O-MINIMALITY? Harvey M. Friedman*
• 2.7. IBRT in A1,...,Ak,fA1,...,fAk,. In this section, we analyze IBRT in A1,...,Ak,fA1,...,fAk,
• INTERPRETING SET THEORY IN DISCRETE MATHEMATICS
• UNPROVABLE THEOREMS IN DISCRETE MATHEMATICS Harvey M. Friedman
• SELECTION FOR BOREL RELATIONS Harvey M. Friedman*
• APPLICATIONS OF LARGE CARDINALS TO BOREL FUNCTIONS
• FINITE TREES AND THE NECESSARY USE OF LARGE CARDINALS
• TRANSFER PRINCIPLES IN SET THEORY Harvey M. Friedman
• ENORMOUS INTEGERS IN REAL LIFE Harvey M. Friedman
• A BIG DIFFERENCE BETWEEN INTERPRETABILITY AND DEFINABILITY IN AN EXPANSION OF THE REAL FIELD
• EXTREMELY LARGE CARDINALS IN THE RATIONALS
• SOME HISTORICAL PERSPECTIVES ON CERTAIN INCOMPLETENESS Harvey M. Friedman
• Harvey M. Friedman Ohio State University
• SEARCH FOR CONSEQUENCES Harvey M. Friedman
• METAMATHEMATICS OF ULM THEORY Harvey M. Friedman
• 5.3. Countable nonstandard models with limited indiscernibles.
• CONCEPT CALCULUS Harvey M. Friedman
• FROMAL STATEMENTS OF GODEL'S SECOND INCOMPLETENESS THEOREM
• Philosophy 532 and Philosophy 536 were the two seminars I presented while on leave at the Princeton University
• INTRODUCTION CONCRETE MATHEMATICAL INCOMPLETENESS
• MY FORTY YEARS ON HIS SHOULDERS Harvey M. Friedman*
• THE INTERPRETATION OF SET THEORY IN MATHEMATICAL
• THE INEVITABILITY OF LOGICAL STRENGTH: strict reverse mathematics
• THE AXIOMATIZATION OF SET THEORY BY EXTENSIONALITY, SEPARATION, AND REDUCIBILITY
• 3.15. Some Observations. Recall the Template and Extended Template introduced at the
• A COMPLETE THEORY OF EVERYTHING: satisfiability in the universal domain
• THE ACKERMANN FUNCTION IN ELEMENTARY ALGEBRAIC GEOMETRY Harvey M. Friedman
• THREE QUANTIFIER SENTENCES Harvey M. Friedman*
• 2.6. EBRT in A1,...,Ak,fA1,...,fAk, on In this section, we use the tree methodology presented in
• Recall the AA table from section 3.3. 1. A . fA A . gA. INF. AL. ALF. FIN. NON.
• Recall the reduced AA table from section 3.4. 1. B . fA A . gA. INF. AL. ALF. FIN. NON.
• GODEL'S LEGACY IN MATHEMATICAL Harvey M. Friedman
• COMPUTER ASSISTED CERTAINTY Harvey M. Friedman
• ADVENTURES IN LOGIC FOR UNDERGRADUATES
• [Al16] P. Aleksandrov, Sur la puissance des ensembles mesurables, Bulletin Comptes Rendus Hebdomadaires des
• EXTREMELY LARGE CARDINALS IN THE RATIONALS
• 1.4. Thin Set Theorems. Recall the Thin Set Theorem from section 1.1.
• ISSUES IN THE FOUNDATIONS OF MATHEMATICS Harvey M. Friedman
• arXiv:0805.1386v2[cs.LO]26Aug2008 A language for mathematical
• Harvey M. Friedman Ohio State University
• INTRODUCTION TO BRT 1.1. General Formulation.
• CLASSIFICATIONS 2.1. Methodology.
• 5.7. Transfinite induction, comprehension, indiscernibles, infinity, 0
• BOOLEAN RELATION INCOMPLETENESS
• COMBINATORIAL SET THEORETIC PRINCIPLES
• ON EXPANSIONS OF O-MINIMAL STRUCTURES PRELIMINARY REPORT
• THE FORMALIZATION OF MATHEMATICS Harvey M. Friedman
• APPLICATIONS OF LARGE CARDINALS TO GRAPH THEORY
• SUBTLE CARDINALS AND LINEAR Harvey M. Friedman
• LONG FINITE SEQUENCES Harvey M. Friedman*
• A BIG DIFFERENCE BETWEEN INTERPRETABILITY AND DEFINABILITY IN AN EXPANSION OF THE REAL FIELD
• BOREL AND BAIRE REDUCIBILITY Harvey M. Friedman
• METAMATHEMATICS OF COMPARABILITY Harvey M. Friedman
• PRIMITIVE INDEPENDENCE RESULTS Harvey M. Friedman
• Philosophy 532 and Philosophy 536 were the two seminars I presented while on leave at the Princeton University
• RESTRICTIONS AND EXTENSIONS Harvey M. Friedman
• SIMILAR SUBCLASSES Harvey M. Friedman
• The number of certain integral polynomials and nonrecursive sets of integers, part 2
• STRICT REVERSE MATHEMATICS Harvey M. Friedman
• 1 INCOMPLETENESS: finite set equations Harvey M. Friedman
• P01 INCOMPLETENESS: finite graph theory 1 Harvey M. Friedman
• INTERPRETATIONS, ACCORDING TO TARSKI Harvey M. Friedman*
• ADJACENT RAMSEY THEORY Harvey M. Friedman*
• EQUATIONAL REPRESENTATIONS Harvey M. Friedman*
• THE UPPER SHIFT KERNEL THEOREMS Harvey M. Friedman*
• RAMSEY THEORY AND ENORMOUS LOWER BOUNDS Harvey M. Friedman
• AXIOMATIZATION OF SET THEORY BY EXTENSIONALITY, SEPARATION, AND REDUCIBILITY
• FROM RUSSELL'S PARADOX TO HIGHER SET THEORY
• FINITE TREES AND THE NECESSARY USE OF LARGE CARDINALS Harvey M. Friedman
• A LOGICIAN LOOKS AT PROGRAMMING Harvey M. Friedman
• DOES MATHEMATICS NEED NEW AXIOMS? ASL Meeting, Urbana
• LECTURE NOTES ON BABY BOOLEAN RELATION THEORY* Harvey M. Friedman
• WHAT YOU CANNOT PROVE 1: before 2000 Harvey M. Friedman
• MY FORTY YEARS ON HIS SHOULDERS Harvey M. Friedman
• NOTE: This talk was prepared at the requrest of the organizers of the Gdel Centenary, in case Professor Georg
• REMARKS ON THE UNKNOWABLE Harvey M. Friedman
• CONTEMPORARY PERSPECTIVES ON HILBERT'S SECOND PROBLEM AND THE GDEL
• LIMITATIONS ON OUR UNDERSTANDING OF THE BEHAVIOR OF SIMPLIFIED PHYSICAL SYSTEMS
• BOOLEAN RELATION Harvey M. Friedman
• STRICT REVERSE MATHEMATICS Harvey M. Friedman
• Harvey M. Friedman Distinguished University Professor
• CONSTRUCTIVE SET THEORY AND BEYOND
• MATHEMATICAL INCOMPLETENESS
• ADVENTURES IN LOGIC FOR UNDERGRADUATES
• ADVENTURES IN LOGIC FOR UNDERGRADUATES
• ADVENTURES IN LOGIC FOR UNDERGRADUATES
• ADVENTURES IN LOGIC FOR UNDERGRADUATES
• PAST, PRESENT, AND FUTURE DIRECTIONS IN
• AN APPRECIATION OF HILARY'S MATHEMATICAL WORK
• INTRODUCTION TO BRT 1.1. General Formulation.
• 1.2. Some BRT settings. The BRT settings were defined in Definition 1.11.
• 1.3. Complementation Theorems. Recall the Complementation Theorem from section 1.1. It
• 1.4. Thin Set Theorems. Recall the Thin Set Theorem from section 1.1.
• 2.5. EBRT in A,B,fA,fB, on (ELG,INF). In this section, we use the tree methodology described in
• 6561 CASES OF EQUATIONAL BOOLEAN RELATION THEORY
• 3.2. Some Useful Lemmas. DEFINITION 3.2.1. The standard pairing function on N is the
• Recall the reduced AA table from section 3.4. 1. B . fA A . gA. INF. AL. ALF. FIN. NON.
• Recall the reduced AA table from section 3.4. 1. B . fA A . gA. INF. AL. ALF. FIN. NON.
• Recall the following reduced table for AB from section 3.5. 1. A . fA B . gA. INF. AL. ALF. FIN. NON.
• 3.10. ABAC. Recall the reduced AB table from section 3.5.
• 3.12. ABBC. Recall the following reduced table for AB from section 3.5.
• 3.13. ACBC. Recall the reduced table for AC from section 3.10.
• PROOF OF PRINCIPAL EXOTIC 4.1. Strongly Mahlo Cardinals of Finite Order.
• 4.3. Some Existential Sentences. In this section, we prove a crucial Lemma needed for
• INDEPENDENCE OF EXOTIC CASE 5.1. Proposition C and Length 3 Towers.
• 1 correct internal arithmetic, simplification.
• 5.8. ZFC + V = L, indiscernibles, and 0 correct arithmetic.
• FURTHER RESULTS 6.1. Propositions D-H.
• DECREASING CHAINS OF ALGEBRAIC SETS Harvey M. Friedman
• TRANSFER PRINCIPLES IN SET Harvey M. Friedman
• COMBINATORIAL SET THEORETIC PRINCIPLES
• LECTURE NOTES ON TERM REWRITING AND COMPUTATIONAL COMPLEXITY
• 5.9. ZFC + V = L + {()( is strongly k-Mahlo)}k + TR(0
• 5.3. Countable nonstandard models with limited indiscernibles.
• 5.2. From length 3 towers to length n In this section, we obtain a variant of Lemma 5.1.7 (Lemma
• INDEPENDENCE OF EXOTIC CASE 5.1. Proposition C and Length 3 Towers.
• 6561 CASES OF EQUATIONAL BOOLEAN RELATION THEORY
• 1.2. Some BRT settings. The BRT settings were defined in Definition 1.11.
• INTRODUCTION CONCRETE MATHEMATICAL INCOMPLETENESS
• [Ar59,62] V.I. Arnold, On the representation of continuous functions of three variables by the superpositions of
• INTERPRETING SET THEORY IN ORDINARY CONCEPT CALCULUS
• Recall the reduced AA table from section 3.4. 1. B . fA A . gA. INF. AL. ALF. FIN. NON.
• DISCRETE INDEPENDENCE RESULTS Harvey M. Friedman
• CLASSIFICATIONS 2.1. Methodology.
• EQUATIONAL BOOLEAN RELATION THEORY Harvey M. Friedman
• UNPROVABLE THEOREMS Harvey M. Friedman
• 2.3. EBRT, IBRT in A,fA,fU. We redo section 2.2 for the signature A,fA,fU, with the
• 6.2. Effectivity. We begin with a straightforward effectivity result
• Decision Problems in Strings and Formal Methods
• THE MATHEMATICAL MEANING OF MATHEMATICAL LOGIC Harvey M. Friedman
• CONCRETE INCOMPLETENESS FROM EFA THROUGH LARGE CARDINALS
• 2.4. EBRT in A,B,fA,fB, on (SD,INF). In this section, we use the tree methodology described in
• ON THE EXPANSION (N, +, 2x ) OF PRESBURGER ARITHMETIC
• Note: This is an interim version that corrects the axioms in section 1.1. There was a problem with interpreting the
• APPLICATIONS OF LARGE CARDINALS TO BOREL FUNCTIONS
• The standard axiomatization of mathematics is given by the formal system ZFC, which is read "Zermelo Frankel set
• DECISION PROBLEMS IN EUCLIDEAN GEOMETRY Harvey M. Friedman*
• WORKING WITH NONSTANDARD MODELS Harvey M. Friedman
• Kernel Structure Theory Harvey M. Friedman
• LECTURE NOTES ON ENORMOUS INTEGERS Harvey M. Friedman
• Abstract. We presented a series of four lectures to the Department of Mathematics at Ohio State University,
• 5.8. ZFC + V = L, indiscernibles, and 0 correct arithmetic.
• TRANSFER PRINCIPLES IN SET Harvey M. Friedman
• THE INTERPRETATION OF SET THEORY IN PURE PREDICATION THEORY preliminary report
• ELEMENTAL SENTENTIAL REFLECTION Harvey M. Friedman
• DOES NORMAL MATHEMATICS NEED NEW Harvey M. Friedman*
• BOOLEAN RELATION THEORY AND MORE Harvey M. Friedman
• 5.2. From length 3 towers to length n In this section, we obtain a variant of Lemma 5.1.7 (Lemma
• THE INTERPRETATION OF SET THEORY IN MATHEMATICAL
• FINITE REVERSE MATHEMATICS Harvey M. Friedman*
• SENTENTIAL REFLECTION Harvey M. Friedman
• 5.4. Limited formulas, limited indiscernibles, x-definability, normal form.
• 5.5. Comprehension, indiscernibles. We fix M = (A,<,0,1,+,-,,,log,E,c1,c2,...) and terms
• 3.3. Single Clauses (duplicates). In this section we handle the relatively easy case of
• Some Decision Problems of Enormous Complexity Harvey M. Friedman
• 6.3. A Refutation. In Proposition A, can we replace ELG by the simpler and
• MAXIMAL NONFINITELY GENERATED SUBALGEBRAS Harvey M. Friedman*
• 2.2. EBRT, IBRT in A,fA. This section is intended to be a particularly gentle
• 3.11. ABBA. Recall the reduced AB table from section 3.5.
• CONCEPT CALCULUS APA PANEL on LOGIC IN PHILOSOPHY
• INTRODUCTION CONCRETE MATHEMATICAL INCOMPLETENESS
• BOOLEAN RELATION INCOMPLETENESS
• [Al16] P. Aleksandrov, Sur la puissance des ensembles mesurables, Bulletin Comptes Rendus Hebdomadaires des
• INVARIANT MAXIMAL CLIQUES AND INCOMPLETENESS