Abstract
In the paper we study lattices of axiomatizable classes and relatively axiomatizable classes. This study is based on Formal Concept Analysis [4,5]. The notion of a relatively axiomatizable class is a generalization of such concepts as variety, quasivariety, ∀-axiomatizable class, \(\exists\)-axiomatizable class, \(\Pi^0_n\)-axiomatizable class, \(\Sigma^0_n\)-axiomatizable class and so on. Relatively axiomatizable classes were studied in [10]. It is proved in the paper that any finite lattice may be represented as the lattice of all relatively axiomatizable subclasses of the class of all models of a one-element signature with respect to some set of sentences. Also we prove that any finite or countable complete lattice is isomorphic to the lattice of all relatively axiomatizable subclasses of some class of models with respect to a proper set of sentences.
Supported by RFBR grant N 05-01-04003-NNIO-a (DFG project COMO, GZ: 436 RUS 113/829/0-1).
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Pal’chunov, D.E. (2007). Lattices of Relatively Axiomatizable Classes. In: Kuznetsov, S.O., Schmidt, S. (eds) Formal Concept Analysis. ICFCA 2007. Lecture Notes in Computer Science(), vol 4390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70901-5_15
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DOI: https://doi.org/10.1007/978-3-540-70901-5_15
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