Harvey Friedman's Research on the Foundations of MathematicsL.A. Harrington, M.D. Morley, A. Šcedrov, S.G. Simpson This volume discusses various aspects of Harvey Friedman's research in the foundations of mathematics over the past fifteen years. It should appeal to a wide audience of mathematicians, computer scientists, and mathematically oriented philosophers. |
Contents
| 1 | |
| 11 | |
CHAPTER 3 NONPROVABILITY OF CERTAIN COMBINATORIAL PROPERTIES OF FINITE TREES | 87 |
CHAPTER 4 THE CONSISTENCY STRENGTHS OF SOME FINITE FORMS OF THE HIGMAN AND KRUSKAL THEOREMS | 119 |
CHAPTER 5 FRIEDMANS RESEARCH ON SUBSYSTEMS OF SECOND ORDER ARITHMETIC | 137 |
CHAPTER 6 BOREL STRUCTURES FOR FIRSTORDER AND EXTENDED LOGICS | 161 |
CHAPTER 7 NONSTANDARD MODELS AND RELATED DEVELOPMENTS | 179 |
CHAPTER 8 INTUITIONISTIC FORMAL SYSTEMS | 231 |
CHAPTER 11 COMPUTATIONAL COMPLEXITY OF REAL FUNCTIONS | 309 |
CHAPTER 12 THE PEBBLE GAME AND LOGICS OF PROGRAMS | 317 |
CHAPTER 13 EQUALITY BETWEEN FUNCTIONALS REVISITED | 331 |
CHAPTER 14 MATHEMATICAL ASPECTS OF RECURSIVE FUNCTION THEORY | 339 |
CHAPTER 15 BIG NEWS FROM ARCHIMEDES TO FRIEDMAN | 353 |
CHAPTER 16 SOME RAPIDLY GROWING FUNCTIONS | 367 |
CHAPTER 17 THE VARIETIES OF ARBOREAL EXPERIENCE | 381 |
CHAPTER 18 DOES GÖDELS THEOREM MATTER TO MATHEMATICS? | 399 |
CHAPTER 9 INTUITIONISTIC SET THEORY | 257 |
CHAPTER 10 ALGORITHMIC PROCEDURES GENERALIZED TURING ALGORITHMS AND ELEMENTARY RECURSION THEORY | 285 |
HARVEY FRIEDMANS PUBLICATIONS | 405 |
Common terms and phrases
algorithm analysis ATRo axioms binary Borel function Borel model bounded classical combinatorial completeness computable function consistency construction countable defined definition denote elements embedding equivalent existence finite trees first-order first-order logic formal systems formula function f Gödel's Harrington Harvey Friedman infinite integers interpretation intuitionistic logic isomorphic Kreisel Kripke models Kruskal's Theorem Lemma Math model theory models of arithmetic n e º natural numbers nodes nonstandard models North-Holland notation notion obtain ordinal Paris-Harrington Theorem partial functions partial recursive functions Peano arithmetic polynomial time computable predicate primitive recursive proof of Theorem properties Proposition H provable prove quantifiers Ramsey's Theorem real numbers recursion theory recursively enumerable relation Reverse Mathematics satisfies second order arithmetic sentences sequence set theory stack statement structure subset subsystems Symbolic Logic there's totally Borel transfinite induction translation Turing degrees uncountable variables