Abstract.
We use the theory of domains with totality to construct some logics generalizing ω-logic and β-logic and we prove a completenes theorem for these logics. The key application is E-logic, the logic related to the functional 3 E. We prove a compactness theorem for sets of sentences semicomputable in 3 E.
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Received: 21 January 1998 / Published online: 2 September 2002
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Normann, D. Continuity, proof systems and the theory of transfinite computations. Arch. Math. Logic 41, 765–788 (2002). https://doi.org/10.1007/s001530200138
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DOI: https://doi.org/10.1007/s001530200138