A new Löwenheim-Skolem theorem
نویسندگان
چکیده
منابع مشابه
Downward Löwenheim-Skolem Theorem and interpolation in logics with constructors
The present paper describes a method for proving Downward Löwenheim-Skolem Theorem within an arbitrary institution satisfying certain logic properties. In order to demonstrate the applicability of the present approach, the abstract results are instantiated to many-sorted first-order logic and preorder algebra. In addition to the first technique for proving Downward Löwenheim-Skolem Theorem, ano...
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This paper establishes a refinement of the classical LöwenheimSkolem theorem. The main result shows that any first order structure has a countable elementary substructure with strong second order properties. Several consequences for Singular Cardinals Combinatorics are deduced from this.
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We discuss several possible extensions of the classical LöwenheimSkolem Theorem to finite structures and give a counterexample refuting almost all of them. Mathematics Subject Classification: 03C13, 03C95
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We present a model-theoretic property of finite structures, that can be seen to be a finitary analogue of the well-studied downward Löwenheim-Skolem property from classical model theory. We call this property the L-equivalent bounded substructure property, denoted L-EBSP, where L is either FO or MSO. Intuitively, L-EBSP states that a large finite structure contains a small “logically similar” s...
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This paper is a contribution to the model theory of non-classical firstorder predicate logics. In a wide framework of first-order systems based on algebraizable logics, we study several notions of homomorphisms between models and find suitable definitions of elementary homomorphism, elementary substructure and elementary equivalence. Then we obtain (downward and upward) Löwenheim–Skolem theorem...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2004
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-04-03445-2