Abstract
There is no known syntactic characterization of the class of finite definitions in terms of a set of basic definitions and a set of basic operators under which the class is closed. Furthermore, it is known that the basic propositional operators do not preserve finiteness. In this paper I survey these problems and explore operators that do preserve finiteness. I also show that every definition that uses only unary predicate symbols and equality is bound to be finite.
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Martinez, M. Some Closure Properties of Finite Definitions. Studia Logica 68, 43–68 (2001). https://doi.org/10.1023/A:1011998021743
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DOI: https://doi.org/10.1023/A:1011998021743