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Lattice of Algebraically Closed Sets in One-Based Theories

Lee Fong Low
The Journal of Symbolic Logic
Vol. 59, No. 1 (Mar., 1994), pp. 311-321
DOI: 10.2307/2275268
Stable URL: http://www.jstor.org/stable/2275268
Page Count: 11
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Lattice of Algebraically Closed Sets in One-Based Theories
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Abstract

Let T be a one-based theory. We define a notion of width, in the case of T having the finiteness property, for the lattice of finitely generated algebraically closed sets and prove Theorem. Let T be one-based with the finiteness property. If T is of bounded width, then every type in T is nonorthogonal to a weight one type. If T is countable, the converse is true.

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