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  1. The Formal Layer of {Brain and Mind} and Emerging Consciousness in Physical Systems.Jerzy Król & Andrew Schumann - forthcoming - Foundations of Science:1-30.
    We consider consciousness attributed to systems in space-time which can be purely physical without biological background and focus on the mathematical understanding of the phenomenon. It is shown that the set theory based on sets in the foundations of mathematics, when switched to set theory based on ZFC models, is a very promising mathematical tool in explaining the brain/mind complex and the emergence of consciousness in natural and artificial systems. We formalise consciousness-supporting systems in physical space-time, but this is localised (...)
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  • Random World and Quantum Mechanics.Jerzy Król, Krzysztof Bielas & Torsten Asselmeyer-Maluga - 2023 - Foundations of Science 28 (2):575-625.
    Quantum mechanics (QM) predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin–Löf. We extend this result and demonstrate that QM is algorithmic $$\omega$$ -random and generic, precisely as described by the ’miniaturisation’ of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo–Fraenkel Solovay random on (...)
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