# Definitions for categoricitycat·e·goric·i·ty

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1. categoricitynoun

The quality of being categorical.

### WikipediaRate this definition:0.0 / 0 votes

1. categoricity

In mathematical logic, a theory is categorical if it has exactly one model (up to isomorphism). Such a theory can be viewed as defining its model, uniquely characterizing the model's structure. In first-order logic, only theories with a finite model can be categorical. Higher-order logic contains categorical theories with an infinite model. For example, the second-order Peano axioms are categorical, having a unique model whose domain is the set of natural numbers N . {\displaystyle \mathbb {N} .} In model theory, the notion of a categorical theory is refined with respect to cardinality. A theory is κ-categorical (or categorical in κ) if it has exactly one model of cardinality κ up to isomorphism. Morley's categoricity theorem is a theorem of Michael D. Morley (1965) stating that if a first-order theory in a countable language is categorical in some uncountable cardinality, then it is categorical in all uncountable cardinalities. Saharon Shelah (1974) extended Morley's theorem to uncountable languages: if the language has cardinality κ and a theory is categorical in some uncountable cardinal greater than or equal to κ then it is categorical in all cardinalities greater than κ.

### Numerology

1. Chaldean Numerology

The numerical value of categoricity in Chaldean Numerology is: 8

2. Pythagorean Numerology

The numerical value of categoricity in Pythagorean Numerology is: 9

## Translations for categoricity

• قطعية
• வகைப்பாடு

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"categoricity." Definitions.net. STANDS4 LLC, 2024. Web. 13 Jun 2024. <https://www.definitions.net/definition/categoricity>.

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