PRINCIPIA MATHEMATICA

By PATRICIA CLARK

CONTENTS MATHEMATICIAN’S WORLD MATHEMATICAL STRUCTURES EVERYTHING IS A SET ANTINOMIES OF SET THEORY THE AXIOMATIC METHOD THE NECESSITY OF USING ABSTRACT CONCEPTS MAIN POINTS OF THE CHAPTER LANGUAGE, LOGIC AND COMPUTATIONS THE LANGUAGE OF MATHEMATICS TRUTH AND MODELS PROOFS PROGRAMS AND COMPUTATIONS THE LAMBDA CALCULUS SET THEORY THE AXIOMS OF SET THEORY THE ARITHMETIC OF IN?NITY WHAT IS THE LARGEST NUMBER? CONTROVERSIAL AXIOMS ALTERNATIVE SET-THEORETICAL FOUNDATIONS PROOFS OF IMPOSSIBILITY IMPOSSIBILITY PROOFS IN GEOMETRY AND ALGEBRA THE INCOMPLETENESS THEOREMS ALGORITHMICALLY UNSOLVABLE PROBLEMS CONCRETE INDEPENDENCE THE INDEPENDENT SENTENCES OF SET THEORY THE COMPLEXITY OF COMPUTATIONS WHAT IS COMPLEXITY? RANDOMNESS, INTERACTION AND CRYPTOGRAPHY PARALLEL COMPUTATIONS QUANTUM COMPUTATIONS DESCRIPTIONAL COMPLEXITY PROOF COMPLEXITY PROOF THEORY THEORIES AND COMPLEXITY CLASSES PROPOSITIONAL PROOFS FEASIBLE INCOMPLETENESS CONSISTENCY, TRUTH AND EXISTENCE CONSISTENCY AND EXISTENCE THE ATTRIBUTES OF REALITY FINITISM AND PHYSICAL REALITY BIBLIOGRAPHICAL REMARKS REFERENCES