Some closure properties of finite definitions

Studia Logica 68 (1):43-68 (2001)

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.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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Reprint years 2004
DOI 10.1023/A:1011998021743
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Guest Editors’ Introduction.Riccardo Bruni & Shawn Standefer - 2019 - Journal of Philosophical Logic 48 (1):1-9.
Conditionals in Theories of Truth.Anil Gupta & Shawn Standefer - 2017 - Journal of Philosophical Logic 46 (1):27-63.
Solovay-Type Theorems for Circular Definitions.Shawn Standefer - 2015 - Review of Symbolic Logic 8 (3):467-487.
Finite Circular Definitions.Anil Gupta - 2006 - In Thomas Bolander, Vincent F. Hendricks & Stig Andur Andersen (eds.), Self-Reference. CSLI Publications. pp. 79-93.
Non-Classical Circular Definitions.Shawn Standefer - 2017 - Australasian Journal of Logic 14 (1).

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