Titlebook: Collegium Logicum; Kurt-G?del-Gesellschaft Conference proceedings 1996 Springer-Verlag/Wien 1996 Resolution.Turing machine.complexity.comp

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The Craig Interpolation Theorem for Schematic Systems,on system and the operation of substitution of terms and formulas in it. We show a generalization of the Craig Interpolation Theorem for a natural class of schematic systems while we determine sufficient conditions for a schematic system to enjoy Interpolation. These conditions are much weaker than

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Numbers Defined by Turing Machines,g machine mappings. Using the interpretation of infinite words as the expansions of numbers we obtain three classes of real respectively complex numbers. We prove that the three classes of complex numbers form algebraically closed subfields of the field of complex numbers.

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Resolution Games and Non-Liftable Resolution Orderings, additional rules, as for example saturation. This is possible because of a new proof method which avoids making use of the standard ordered lifting theorem. This new proof method is based on a new technique, which we call the resolution game.

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Collegium Logicum978-3-7091-9461-4Series ISSN 0947-577X

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