Gödel and the Incompleteness of Arithmetic  

作　　者：Pinheiro ;Pinheiro(IICSE University, Wilmington, USA)

机构地区：[1]IICSE University, Wilmington, USA

出　　处：《Advances in Pure Mathematics》2016年第8期537-545,共9页理论数学进展（英文）

摘　　要：People normally believe that Arithmetic is not complete because GÖdel launched this idea a long time ago, and it looks as if nobody has presented sound evidence on the contrary. We here intend to do that perhaps for the first time in history. We prove that what Stanford Encyclopedia has referred to as Theorem 3 cannot be true, and, therefore, if nothing else is presented in favour of GÖdel’s thesis, we actually do not have evidence on the incompleteness of Arithmetic: All available evidence seems to point at the extremely opposite direction.People normally believe that Arithmetic is not complete because GÖdel launched this idea a long time ago, and it looks as if nobody has presented sound evidence on the contrary. We here intend to do that perhaps for the first time in history. We prove that what Stanford Encyclopedia has referred to as Theorem 3 cannot be true, and, therefore, if nothing else is presented in favour of GÖdel’s thesis, we actually do not have evidence on the incompleteness of Arithmetic: All available evidence seems to point at the extremely opposite direction.

关 键 词：Gödel ARITHMETIC Peano AXIOM Classical Logic 

分 类 号：O17[理学—数学]