Categoricity

History and Philosophy of Logic 1 (1):187-207 (1980)
Abstract
After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences). The third section deals with applications especially those involving the distinction between characterizing a system and axiomatizing the truths of a system
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References found in this work BETA
Alonzo Church (1956). Introduction to Mathematical Logic. Princeton, Princeton University Press.
Alonzo Church (1944). Introduction to Mathematical Logic. London, H. Milford, Oxford University Press.
John Corcoran (1972). Conceptual Structure of Classical Logic. Philosophy and Phenomenological Research 33 (1):25-47.
Erik Ellentuck (1976). Categoricity Regained. Journal of Symbolic Logic 41 (3):639-643.

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