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  1. Отвъд машината на Тюринг: квантовият компютър.Vasil Penchev - 2014 - Sofia: BAS: ISSK (IPS).
    Quantum computer is considered as a generalization of Turing machine. The bits are substituted by qubits. In turn, a "qubit" is the generalization of "bit" referring to infinite sets or series. It extends the consept of calculation from finite processes and algorithms to infinite ones, impossible as to any Turing machines (such as our computers). However, the concept of quantum computer mets all paradoxes of infinity such as Gödel's incompletness theorems (1931), etc. A philosophical reflection on how quantum computer might (...)
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  • Kurt Gödel.Juliette Kennedy - 2008 - Stanford Encyclopedia of Philosophy.
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  • Algorithmic Information Theory and Undecidability.Panu Raatikainen - 2000 - Synthese 123 (2):217-225.
    Chaitin’s incompleteness result related to random reals and the halting probability has been advertised as the ultimate and the strongest possible version of the incompleteness and undecidability theorems. It is argued that such claims are exaggerations.
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  • Tarski and Lesniewski on Languages with Meaning Versus Languages Without Use: A 60th Birthday Provocation for Jan Wolenski.B. G. Sundholm - unknown
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  • A Plea for Logical Atavism.B. G. Sundholm - unknown
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  • What is an Expression?'.B. G. Sundholm - unknown
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  • Quantification for Peirce's Preferred System of Triadic Logic.Atwell R. Turquette - 1981 - Studia Logica 40 (4):373 - 382.
    Without introducing quantifiers, minimal axiomatic systems have already been constructed for Peirce's triadic logics. The present paper constructs a dual pair of axiomatic systems which can be used to introduce quantifiers into Peirce's preferred system of triadic logic. It is assumed (on the basis of textual evidence) that Peirce would prefer a system which rejects the absurd but tolerates the absolutely undecidable. The systems which are introduced are shown to be absolutely consistent, deductively complete, and minimal. These dual axiomatic systems (...)
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  • Measure Independent Gödel Speed‐Ups and the Relative Difficulty of Recognizing Sets.Martin K. Solomon - 1993 - Mathematical Logic Quarterly 39 (1):384-392.
    We provide and interpret a new measure independent characterization of the Gödel speed-up phenomenon. In particular, we prove a theorem that demonstrates the indifference of the concept of a measure independent Gödel speed-up to an apparent weakening of its definition that is obtained by requiring only those measures appearing in some fixed Blum complexity measure to participate in the speed-up, and by deleting the “for all r” condition from the definition so as to relax the required amount of speed-up. We (...)
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  • On Me Number of Steps in Proofs.Jan Krajíèek - 1989 - Annals of Pure and Applied Logic 41 (2):153-178.
    In this paper we prove some results about the complexity of proofs. We consider proofs in Hilbert-style formal systems such as in [17]. Thus a proof is a sequence offormulas satisfying certain conditions. We can view the formulas as being strings of symbols; hence the whole proof is a string too. We consider the following measures of complexity of proofs: length , depth and number of steps For a particular formal system and a given formula A we consider the shortest (...)
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  • A Connection Between Blum Speedable Sets and Gödel's Speed-Up Theorem.Martin K. Solomon - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (5):417-421.
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