丘奇的论点受到新计算范式的质疑
Church's thesis is questioned by new calculation paradigm
摘要：
丘奇的论文声称所有有效可计算的函数都是递归的。递归函数的各种定义的一个缺点在于，它不是一个语法检查的问题，以找出一个实体是否产生了一个函数。八个新的想法，一个精确的设置算术逻辑和它的元语言给出了适当的环境，建设一个特殊的计算机，ARBACUS计算机。计算机不需要停止;要求计算器以计算机为基础构建，使其总是停止，然后所有计算都有效。仲裁器被定义为具有两层计算的计算器。它允许计算所有原始递归函数，但多级仲裁也允许计算其他非原始递归的仲裁函数。新的计算范式没有上述缺点。教会的论文的捍卫者面临的挑战表明，异国情调的仲裁功能是递归的，并提出了一个递归功能，是不是仲裁。一个包含对角化的三层多级仲裁的构造导致了一个奢侈但可计算的Snark函数，它不是仲裁的。只要它不是表明，所有外来的仲裁功能，特别是Snark函数是算术表示的哥德尔的第一个不完全句是在地狱。
英文摘要：
Church's thesis claims that all effecticely calculable functions are recursive. A shortcoming of the various definitions of recursive functions lies in the fact that it is not a matter of a syntactical check to find out if an entity gives rise to a function. Eight new ideas for a precise setup of arithmetical logic and its metalanguage give the proper environment for the construction of a special computer, the ARBACUS computer. Computers do not come to a necessary halt; it is requested that calculators are constructed on the basis of computers in a way that they always come to a halt, then all calculations are effective. The ARBATOR is defined as a calculator with two-layer-computation. It allows for the calculation of all primitive recursive functions, but multi-level-arbation also allows for the calculation of other arbative functions that are not primitive recursive. The new paradigm of calculation does not have the above mentioned shortcoming. The defenders of Church's thesis are challenged to show that exotic arbative functions are recursive and to put forward a recursive function that is not arbative. A construction with three-tier-multi-level-arbation that includes a diagonalisation leads to the extravagant yet calculable Snark-function that is not arbative. As long as it is not shown that all exotic arbative functions and particularily the Snark-function are arithmetically representable Goedel's first incompleteness sentence is in limbo.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
