A property of stable theories
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چکیده
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Every countable, strictly stable theory either has the Dimensional Order Property (DOP), is deep, or admits an ‘abelian group witness to unsuperstability’. To obtain this and other results, we develop the notion of a ‘regular ideal’ of formulas and study types that are minimal with respect to such an ideal.
متن کاملTheories with the Independence Property
A first-order theory T has the Independence Property provided T ⊢ (Q)(Φ ⇒ Φ1 ∨ · · · ∨ Φn) implies T ⊢ (Q)(Φ ⇒ Φi) for some i whenever Φ,Φ1, . . . ,Φn are formulae of a suitable type and (Q) is any quantifier sequence. Variants of this property have been noticed for some time in logic programming and in linear programming. We show that a first order theory has the independence property for the ...
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1 ω Stable/Totally Transcendental Theories Throughout let T be a complete theory in a countable language L having infinite models. For an L-structure M and A ⊆ M let SM n (A) denote the set of n-types of A. We define a topology (called Stone topology) on SM n (A) by setting basic open sets to be of the form Uφ = {p ∈ SM n (A) : φ ∈ p} where φ is an L(A)-formula. Then SM n (A) is totally disconn...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1972
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-77-1-9-20