We examine whether some well-known properties of partial recursive functions are valid for ITBM-computable functions, i.e., functions which can be computed with infinite time Blum–Shub–Smale machines. It is shown that properties of graphs of ITBM-computable functions differ from the usual properties of graphs of partial recursive functions. All possible ranges of ITBM-computable functions are described, and we consider the existence problem for ITBM-computable bijections between ITBM-computable sets of the same cardinality.

中文翻译：

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ITBM可计算性的特征。一世

我们检查了部分递归函数的某些众所周知的属性是否适用于ITBM可计算的函数，即可以用无限时间的Blum–Shub–Smale机器计算的函数。结果表明，ITBM可计算函数图的性质与部分递归函数图的通常性质不同。描述了ITBM可计算功能的所有可能范围，并且我们考虑了相同基数的ITBM可计算集之间ITBM可计算双射的存在问题。