منابع مشابه
Notes on totally categorical theories
Cherlin, Harrington and Lachlan’s paper on ω0-categorical, ω0-stable theories ([CHL]) was the starting point of geometrical stability theory. The progress made since then allows us better to understand what they did in modern terms (see [PI]) and also to push the description of totally categorical theories further, (see [HR1, AZ1, AZ2]). The first two sections of what follows give an exposition...
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As was shown in [2], totally categorical structures (i.e. which are categorical in all powers) are not finitely axiomatizable. On the other hand, the most simple totally categorical structures: infinite sets, infinite projective or affine geometries over a finite field, are quasi finitely axiomatizable (i.e. axiomatized by a finite number of axioms and the schema of infinity, we will use the ab...
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In the analysis of the structure of totally categorical first order theories, the second author showed that certain combinatorial counting functions play an important role. Those functions are invariants of the structures and are always polynomials in one or many variables, depending on the number of independent dimensions of the theory in question. The first author introduced the notion of gra...
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We show: Theorem 0.1. Let K be a fully LS(K)-tame and short abstract elementary class (AEC) with amalgamation. Write H1 := i(2LS(K))+ and assume that K is categorical in some λ ≥ H1. The following are equivalent: (1) K≥H1 has primes over sets of the form M ∪ {a}. (2) K is categorical in all λ′ ≥ H1. Note that (1) implies (2) appears in an earlier paper. Here we prove (2) implies (1), generalizi...
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A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure S has a core, i.e., S has an endomorphism e such that the structure induced by e(S) is a core; moreover, the core is unique up to isomorphism. We prove that every ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1989
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1989-0943605-1