Embeddings between the elementary ontology with an atom and the monadic second-order predicate logic

Studia Logica 46 (3):247 - 253 (1987)
Let EOA be the elementary ontology augmented by an additional axiom S (S S), and let LS be the monadic second-order predicate logic. We show that the mapping which was introduced by V. A. Smirnov is an embedding of EOA into LS. We also give an embedding of LS into EOA.
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DOI 10.1007/BF00372549
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Mitio Takano (1991). Syntactical Proof of Translation and Separation Theorems on Subsystems of Elementary Ontology. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (9-12):129-138.

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