论文标题
可证明的总递归函数和基本算术中的MRDP定理及其扩展
The provably total recursive functions and the MRDP theorem in Basic Arithmetic and its extensions
论文作者
论文摘要
我们研究了W. Ruitenburg引入的基本算术，文学学士学位。 BA是基于基本逻辑的算术理论，比直觉逻辑弱。我们表明，BA的可证明的总递归函数的类别是原始递归函数的适当子类。研究了三个称为BA+U，BA_C和EBA的BA扩展，并与其可证明的总递归功能有关。结果表明，这三个BA扩展的总递归函数正是原始递归函数。此外，除其他外，还表明，著名的MRDP定理在BA，BA+U，BA_C中不存在，而是在EBA中。
We study Basic Arithmetic, BA introduced by W. Ruitenburg. BA is an arithmetical theory based on basic logic which is weaker than intuitionistic logic. We show that the class of the provably total recursive functions of BA is a proper sub-class of the primitive recursive functions. Three extensions of BA, called BA+U, BA_c and EBA are investigated with relation to their provably total recursive functions. It is shown that the provably total recursive functions of these three extensions of BA are exactly the primitive recursive functions. Moreover, among other things, it is shown that the well-known MRDP theorem does not hold in BA, BA+U, BA_c, but holds in EBA.
