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  1. Consistency and interpolation in linear continuous logic.Mahya Malekghasemi & Seyed-Mohammad Bagheri - 2023 - Archive for Mathematical Logic 62 (7):931-939.
    We prove Robinson consistency theorem as well as Craig, Lyndon and Herbrand interpolation theorems in linear continuous logic.
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  • Extreme types and extremal models.Seyed-Mohammad Bagheri - 2024 - Annals of Pure and Applied Logic 175 (7):103451.
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  • The isomorphism theorem for linear fragments of continuous logic.Seyed-Mohammad Bagheri - 2021 - Mathematical Logic Quarterly 67 (2):193-205.
    The ultraproduct construction is generalized to p‐ultramean constructions () by replacing ultrafilters with finitely additive measures. These constructions correspond to the linear fragments of continuous logic and are very close to the constructions in real analysis. A powermean variant of the Keisler‐Shelah isomorphism theorem is proved for. It is then proved that ‐sentences (and their approximations) are exactly those sentences of continuous logic which are preserved by such constructions. Some other applications are also given.
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  • Maximality of linear continuous logic.Mahya Malekghasemi & Seyed-Mohammad Bagheri - 2018 - Mathematical Logic Quarterly 64 (3):185-191.
    The linear compactness theorem is a variant of the compactness theorem holding for linear formulas. We show that the linear fragment of continuous logic is maximal with respect to the linear compactness theorem and the linear elementary chain property. We also characterize linear formulas as those preserved by the ultramean construction.
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