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  1.  8
    A Foundation for Real Recursive Function Theory.José Félix Costa, Bruno Loff & Jerzy Mycka - 2009 - Annals of Pure and Applied Logic 160 (3):255-288.
    The class of recursive functions over the reals, denoted by , was introduced by Cristopher Moore in his seminal paper written in 1995. Since then many subsequent investigations brought new results: the class was put in relation with the class of functions generated by the General Purpose Analogue Computer of Claude Shannon; classical digital computation was embedded in several ways into the new model of computation; restrictions of were proved to represent different classes of recursive functions, e.g., recursive, primitive recursive (...)
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  2.  10
    Analog Computation and Church's Thesis.Jerzy Mycka - 2006 - In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. pp. 1--331.
  3.  2
    Universality of Functional Systems and Totality of Their Elements – the Limits of Conflict and Mutual Influence.Jerzy Mycka - 2017 - Philosophical Problems in Science 63:31-58.
    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 (...)
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    Uniwersalność systemów funkcyjnych a całkowitość dziedzin funkcji – granice konfliktu i wzajemnego wpływu.Jerzy Mycka - 2017 - Philosophical Problems in Science 63:31-58.
    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 (...)
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  5. Czy muzyka jest ucieleśnieniem matematyki? Analiza przypadku introitu Statuit.Jerzy Mycka - 2012 - Filozofia Nauki 20 (3).
    The article starts with various definitions of music and its components (taken es-pecially from medieval sources). Then the Statuit introit is presented as the main example useful for mathematical analysis in the paper. We discuss the distinc-tion between a musical work and its performance and give a review of possible representations/ notations of music with their short mathematical characteristics. The next point is devoted to the concept of modality, Gregorian scales and selected theories linking musical experience with mathematics. We use (...)
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  6. Is Music Embodied Mathematics? Case Study of the Statuit Introit.Agnieszka Mycka & Jerzy Mycka - 2012 - Filozofia Nauki 20 (3).
     
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