Definitions
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 noun The quality of being
categorical .
Etymologies
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Examples

(Discussion of Hellman 1989 will be reserved for Section 5.2, when the notion of categoricity is introduced.) 4.5 Fictionalism

In turn, Dedekind is much more explicit and clear than Frege about issues such as categoricity, completeness, independence, etc., which puts him in proximity with a “formal axiomatic” approach as championed later by Hilbert and Bernays

It is closer in kind to what is termed "categoricity" in formal semantics, a categorical theory being one whose models are all isomorphic to one another.

Often acknowledged in that connection are: his analysis of the notion of continuity, his introduction of the real numbers by means of Dedekind cuts, his formulation of the DedekindPeano axioms for the natural numbers, his proof of the categoricity of these axioms, and his contributions to the early development of set theory

In Dedekind's case, completeness is to be understood in a semantic sense, as based on categoricity; similarly, consistency is to be understood semantically, as satisfiability by a system of objects

Against this account, however, it may be pointed out that it seems that the categoricity of intended models for real analysis, for instance, cannot be ensured in this manner.

One of the main consequences of the completeness theorem is that categoricity fails for Peano arithmetic and for ZermeloFraenkel set theory.

GÃ¶del in his review (1934c) of Skolem's paper also does not mention this fact, rather observing that the failure of categoricity for arithmetic follows from the incompleteness theorem.

Predicability, then, is not a sufficient condition of categoricity, but nonpredicability is a sufficient disqualification.

It played a major role in debates over the ontology of general relativity and was an important part of the background to the development of the modern concept of categoricity in formal semantics (for more on the history, influence, and demise of the principle of univocalness, see Howard 1992 and 1996).
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