The Foundations of Mathematics in the Theory of Sets

• Author(s): John P. Mayberry,
• Publisher: Cambridge University Press
• Pages: 424
• ISBN_10: 0521770343
  ISBN_13: 9780521770347
  
• Language: en
• Categories: Mathematics / Logic , Mathematics / Set Theory , Medical / General , Philosophy / General ,

Description:... This book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. The author investigates the logic of quantification over the universe of sets and discusses its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. Suitable for graduate students and researchers in both philosophy and mathematics.