01481nmm a2200241 u 4500001001200000003002700012005001700039007002400056008004100080020001800121050001000139100002200149245007200171260004800243300002700291653001500318041001900333989003200352490005300384856006300437082001200500520072700512EB001382968EBX0100000000000000090593300000000000000.0cr|||||||||||||||||||||170324 ||| eng a9781139087124 4aQA2481 aMayberry, John P.00aThe foundations of mathematics in the theory of setscJ.P. Mayberry aCambridgebCambridge University Pressc2000 axx, 424 pagesbdigital aSet theory07aeng2ISO 639-2 bCBOaCambridge Books Online0 aEncyclopedia of mathematics and its applications uhttps://doi.org/10.1017/CBO9781139087124xVerlag3Volltext0 a511.322 aThis 2001 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'. This leads to an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. The subject matter of the book falls on the borderline between philosophy and mathematics, and should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics