Abstract
Transfer theorems are central results in abstract algebraic logic that allow to generalize properties of the lattice of theories of a logic to any algebraic model and its lattice of filters. Their proofs sometimes require the existence of a natural extension of the logic to a bigger set of variables. Constructions of such extensions have been proposed in particular settings in the literature. In this paper we show that these constructions need not always work and propose a wider setting (including all finitary logics and those with countable language) in which they can still be used.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Cintula, P., P. Hájek, and C. Noguera, (eds.) Handbook of Mathematical Fuzzy Logic (in 2 volumes), vol. 37, 38 of Studies in Logic, Mathematical Logic and Foundations, College Publications, London, 2011.
Cintula P., Noguera C.: Implicational (semilinear) logics I: A new hierarchy. Archive for Mathematical Logic 49(4), 417–446 (2010)
Cintula P., Noguera C.: The proof by cases property and its variants in structural consequence relations. Studia Logica 101(4), 713–747 (2013)
Czelakowski J.: Sentential logics and Maehara Interpolation Property. Studia Logica 44(3), 265–283 (1985)
Czelakowski, J., Protoalgebraic Logics, vol. 10 of Trends in Logic, Kluwer, Dordrecht, 2001.
Font, J. M., and R. Jansana, A General Algebraic Semantics for Sentential Logics, vol. 7 of Lecture Notes in Logic, 2 edn., Association for Symbolic Logic, Ithaca, 2009. Freely downloadable from http://projecteuclid.org/euclid.lnl/1235416965.
Font, J. M., R. Jansana, and D. L. Pigozzi, A survey of Abstract Algebraic Logic, Studia Logica, 74(1–2):13–97, 2003. Special Issue on Abstract Algebraic Logic II.
Font J. M., Jansana R., Pigozzi D.L.: Update to a survey of Abstract Algebraic Logic. Studia Logica 91(1), 125–130 (2009)
Łoś J., Suszko R.: Remarks on sentential logics. Journal of Symbolic Logic 40(4), 603–604 (1975)
Shoesmith D.J., Smiley T.J.: Deducibility and many-valuedness. Journal of Symbolic Logic 36(4), 610–622 (1971)
Author information
Authors and Affiliations
Corresponding author
Additional information
Presented by Jacek Malinowski
Rights and permissions
About this article
Cite this article
Cintula, P., Noguera, C. A Note on Natural Extensions in Abstract Algebraic Logic. Stud Logica 103, 815–823 (2015). https://doi.org/10.1007/s11225-014-9594-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11225-014-9594-8