Universal theories categorical in power and κ-generated models

Steven Givant; Saharon Shelah

doi:10.1016/0168-0072(94)90018-3

Universal theories categorical in power and κ-generated models

Steven Givant^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 (uncountable) 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.

Original language	English
Pages (from-to)	27-51
Number of pages	25
Journal	Annals of Pure and Applied Logic
Volume	69
Issue number	1
DOIs	https://doi.org/10.1016/0168-0072(94)90018-3
State	Published - 6 Sep 1994

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Universal theories categorical in power and κ-generated models

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