A presentation theorem for continuous logic and metric abstract elementary classes

被引：4

作者：

Boney, Will ^{[1
]}

机构：

[1] Harvard Univ, Dept Math, 1 Oxford St, Cambridge, MA 02138 USA

来源：

MATHEMATICAL LOGIC QUARTERLY | 2017年 / 63卷 / 05期

基金：

美国国家科学基金会;

关键词：

CATEGORICITY; STABILITY;

D O I：

10.1002/malq.201600058

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In recent years, model theory has widened its scope to include metric structures by considering real-valued models whose underlying set is a complete metric space. We show that it is possible to carry out this work by giving presentation theorems that translate the two main frameworks (continuous first order logic and Metric Abstract Elementary Classes) into discrete settings (a nice fragment of L-omega 1,L-omega and Abstract Elementary Classes, respectively). We also translate various notions of classification theory. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：397 / 414

页数：18

共 50 条

[1] Metric abstract elementary classes with perturbations
Hirvonen, Asa
Hyttinen, Tapani
[J]. FUNDAMENTA MATHEMATICAE, 2012, 217 (02) : 123 - 170
[2] A stability transfer theorem in d-tame metric abstract elementary classes
Zambrano, Pedro
[J]. MATHEMATICAL LOGIC QUARTERLY, 2012, 58 (4-5) : 333 - 341
[3] METRIC ABSTRACT ELEMENTARY CLASSES AS ACCESSIBLE CATEGORIES
Lieberman, M.
Rosicky, J.
[J]. JOURNAL OF SYMBOLIC LOGIC, 2017, 82 (03) : 1022 - 1040
[4] Limit models in metric abstract elementary classes: the categorical case
Villaveces, Andres
Zambrano, Pedro
[J]. MATHEMATICAL LOGIC QUARTERLY, 2016, 62 (4-5) : 319 - 334
[5] LIMITS OF ABSTRACT ELEMENTARY CLASSES
Lieberman, M.
Rosicky, J.
[J]. THEORY AND APPLICATIONS OF CATEGORIES, 2015, 30 : 1647 - 1658
[6] Quasiminimal abstract elementary classes
Sebastien Vasey
[J]. Archive for Mathematical Logic, 2018, 57 : 299 - 315
[7] Quasiminimal abstract elementary classes
Vasey, Sebastien
[J]. ARCHIVE FOR MATHEMATICAL LOGIC, 2018, 57 (3-4) : 299 - 315
[8] Around independence and domination in metric abstract elementary classes: assuming uniqueness of limit models
Villaveces, Andres
Zambrano, Pedro
[J]. MATHEMATICAL LOGIC QUARTERLY, 2014, 60 (03) : 211 - 227
[9] CLASSIFICATION OF NON ELEMENTARY CLASSES .2. ABSTRACT ELEMENTARY CLASSES
SHELAH, S
[J]. LECTURE NOTES IN MATHEMATICS, 1987, 1292 : 419 - 497
[10] Independence in finitary abstract elementary classes
Hyttinen, T.
Kesala, M.
[J]. ANNALS OF PURE AND APPLIED LOGIC, 2006, 143 (1-3) : 103 - 138

← 1 2 3 4 5 →