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Abstract

We prove completeness, interpolation, decidability and an omitting types theorem for certain multi-dimensional modal logics where the states are not abstract entities but have an inner structure. The states will be sequences. Our approach is algebraic addressing varieties generated by complex algebras of Kripke semantics for such logics. The algebras dealt with are common cylindrification free reducts of cylindric and polyadic algebras. For finite dimensions, we show that such varieties are finitely axiomatizable, have the super amalgamation property, and that the subclasses consisting of only completely representable algebras are elementary, and are also finitely axiomatizable in first order logic. Also their modal logics have an N P complete satisfiability problem. Analogous results are obtained for infinite dimensions by replacing finite axiomatizability by finite schema axiomatizability.

  • [1]

    Ahmed, T. S., Completions, Complete representations and Omitting types, in [2], 186205.

  • [2]

    Andréka, H., Ferenczi, M. and Németi, I. (Editors), Cylindric-like Algebras and Algebraic Logic. Bolyai Society Mathematical Studies 22 (2013).

    • Search Google Scholar
    • Export Citation
  • [3]

    Andréka, H., Németi, I. and Ahmed, T. S., A nonrepresentable infinite dimensional quasi-polyadic equality algebra with a representable cylindric reduct, Studia Scientiarum Mathematicarum Hungarica, 50 (1) (2013), pp. 116.

    • Search Google Scholar
    • Export Citation
  • [4]

    Blackburn, P., De Rijke, M. and Venema, Y., Modal Logic, Cambridge Text in Theoretical Computer Science, Third printing (2008).

  • [5]

    Fremlin, D. H., Consequences of Martin's axiom, Cambridge University Press, 1984.

  • [6]

    Ganyushkin, O. and Mazorchuk, V., Classical Finite Transformation Semi-groups-An Introduction, Springer, 2009.

  • [7]

    Henkin, L., Monk, J. D. and Tarski, A., Cylindric Algebras Part I, North Holland, 1971.

  • [8]

    Henkin, L., Monk, J. D. and Tarski, A., Cylindric Algebras Part II, North Holland, 1985.

  • [9]

    Hirsch, R. and Hodkinson, I., Complete representations in algebraic logic, Journal of Symbolic Logic, 62 (3) (1997), 816847.

  • [10]

    Hirsch, R. and Hodkinson, I., Relation Algebras by Games, Studies In Logic, North Holland 147 (2002).

  • [11]

    Sági, G., Defining relations for non-permutational finite transformations, Semigroup Forum, 58 (1) (1999), 94105.

  • [12]

    Sági, G., A Note on Algebras of Substitutions, Studia Logica, (72)(2) (2002), 265284.

  • [13]

    Sági, G., On nonrepresentable G-polyadic algebras with representable cylindric reducts, Logic Journal of IGPL, 19 (1) (2011), 105109.

    • Search Google Scholar
    • Export Citation

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  • Impact Factor (2019): 0.486
  • Scimago Journal Rank (2019): 0.234
  • SJR Hirsch-Index (2019): 23
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.309
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21
  • SJR Quartile Score (2018): Q3 Mathematics (miscellaneous)

Language: English, French, German

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Publication Programme: 2020. Vol. 57.
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Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

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