Universality of functional systems and totality of their elements – the limits of conflict and mutual influence
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Dec 28, 2017
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Abstract
The article presents several examples of different mathematical structures and interprets their properties related to the existence of universal functions. In this context, relations between the problem of totality of elements and possible forms of universal functions are analyzed. Furthermore, some global and local aspects of the mentioned functional systems are distinguished and compared. In addition, the paper attempts to link universality and totality with the dynamic and static properties of mathematical objects and to consider the problem of limitations in the construction of structures combining harmoniously the availability of information at the local and global level.
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Mycka, J. (2017). Universality of functional systems and totality of their elements – the limits of conflict and mutual influence. Philosophical Problems in Science (Zagadnienia Filozoficzne W Nauce), (63), 31–58. Retrieved from https://zfn.edu.pl/index.php/zfn/article/view/404
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References
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Odifreddi, P., 1992. Classical recursion theory: The theory of functions and sets of natural numbers. Vol. I. Amsterdam: North Holland.
Rogers, H., 1987, Theory of recursive functions and effective computability. Mabridge, Mass.: MIT Press.
Shen, A., Vereshchagin, N., 2002. Computable functions. Providence, RI: American Mathematical Society.