Universal theories categorical in power and κ-generated models

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Annals of Pure and Applied Logic 69 (1):27-51 (1994)
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Abstract

We investigate a notion called uniqueness in power κ that is akin to categoricity in power κ, but is based on the cardinality of the generating sets of models instead of on the cardinality of their universes. The notion is quite useful for formulating categoricity-like questions regarding powers below the cardinality of a theory. We prove, for universal theories T, that if T is κ-unique for one uncountable κ, then it is κ-unique for every uncountable κ; in particular, it is categorical in powers greater than the cardinality of T

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10.1016/0168-0072(94)90018-3

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References found in this work

Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.
Universal horn classes categorical or free in power.Steven Givant - 1978 - Annals of Mathematical Logic 15 (1):1-53.

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