On d-finiteness in continuous structures

Itaï Ben Yaacov, and Alexander Usvyatsov. "On d-finiteness in continuous structures." Fundamenta Mathematicae 194.1 (2007): 67-88. <http://eudml.org/doc/282745>.

@article{ItaïBenYaacov2007,
abstract = {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.},
author = {Itaï Ben Yaacov, Alexander Usvyatsov},
journal = {Fundamenta Mathematicae},
keywords = {continuous first-order logic; approximately -saturated model; -finite tuple; model theory of metric structures},
language = {eng},
number = {1},
pages = {67-88},
title = {On d-finiteness in continuous structures},
url = {http://eudml.org/doc/282745},
volume = {194},
year = {2007},
}

TY - JOUR
AU - Itaï Ben Yaacov
AU - Alexander Usvyatsov
TI - On d-finiteness in continuous structures
JO - Fundamenta Mathematicae
PY - 2007
VL - 194
IS - 1
SP - 67
EP - 88
AB - 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.
LA - eng
KW - continuous first-order logic; approximately -saturated model; -finite tuple; model theory of metric structures
UR - http://eudml.org/doc/282745
ER -