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Titlebook: Combinatorics, Computability and Logic; Proceedings of the T C. S. Calude,M. J. Dinneen,S. Sburlan Conference proceedings 2001 Springer-Ver

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A Highly Random Numberniversal self delimiting machine halts. The algorithmic complexity of . is strictly greater than that of ., but similar to the algorithmic complexity of ., the halting probability of an oracle machine. What makes . interesting is that it is an example of a highly random number definable without considering oracles.
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Architecture and Implementation <1; the 1-mc real numbers are just the semi-computable real numbers and the set of all mc real numbers is contained properly in the set of weakly computable real numbers, where . is weakly computable if there are semi-computable real numbers ., . such that . = . + .. Furthermore, we show also an infinite hierarchy of mc real numbers.
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Overview: 978-1-85233-526-7978-1-4471-0717-0
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Smart-ECO Buildings towards 2020/2030and how the basic ideas and methods used in a restricted area of Logic derive from, or at least interact with, a wider mathematical and intellectual experience. I can only offer suggestions, not scholarly arguments, to those who share my interest.
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https://doi.org/10.1007/978-3-319-06551-9 set . can be ordered with the usual set inclusion relation. We show that this ordered set is a complete lattice whenever . is a complete join-semilattice. We introduce dense sets of an Armstrong system and present some results concerning them. In particular, we characterize keys of a database relation in terms of dense sets.
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