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On d-finiteness in continuous structures

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Yaacov I., Usvyatsov A.

Fundamenta Mathematicae

2007

tom 194

nr 1

67-88

We observe that certain classical results of first order model theory fail in the context of continuous first order logic. We argue that this happens since finite tuples in a continuous structure may behave as infinite tuples in classical model theory. The notion of a d-finite tuple attempts to capture some aspects of the classical finite tuple behaviour. We show that many classical results involving finite tuples are valid in continuous logic upon replacing "finite" with "d-finite". Other results, such as Vaught's no two models theorem and Lachlan's theorem on the number of countable models of a superstable theory are proved under the assumption of enough (uniformly) d-finite tuples.

Thorn orthogonality and domination in unstable theories

100%

Onshuus A., Usvyatsov A.

Fundamenta Mathematicae

2011

tom 214

nr 3

241-268

We study orthogonality, domination, weight, regular and minimal types in the contexts of rosy and super-rosy theories.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Usvyatsov A.

1 Onshuus A.

1 Yaacov I.

1 2011

1 2007

Wyniki wyszukiwania

On d-finiteness in continuous structures

Thorn orthogonality and domination in unstable theories