Nondefinability of Rings of Integers in Most Algebraic Fields

被引：2

作者：

Dittmann, Philip ^{[1
]}

Fehm, Arno ^{[1
]}

机构：

[1] Tech Univ Dresden, Inst Algebra, Fak Math, Dresden, Germany

来源：

NOTRE DAME JOURNAL OF FORMAL LOGIC | 2021年 / 62卷 / 03期

基金：

美国国家科学基金会;

关键词：

definability; pseudo-algebraically closed fields; SUBFIELDS;

D O I：

10.1215/00294527-2021-0029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the set of algebraic extensions F of Q in which Z or the ring of integers O-F are definable is meager in the set of all algebraic extensions.

引用

页码：589 / 592

页数：4

共 15 条

[1] Existentially generated subfields of large fields
Anscombe, Sylvy
[J]. JOURNAL OF ALGEBRA, 2019, 517 : 78 - 94
[2] Generic structures and simple theories
Chatzidakis, Z
Pillay, A
[J]. ANNALS OF PURE AND APPLIED LOGIC, 1998, 95 (1-3) : 71 - 92
[3] Amalgamation of types in pseudo-algebraically closed fields and applications
Chatzidakis, Zoe
[J]. JOURNAL OF MATHEMATICAL LOGIC, 2019, 19 (02)
[4] On model-theoretic tree properties
Chernikov, Artem
Ramsey, Nicholas
[J]. JOURNAL OF MATHEMATICAL LOGIC, 2016, 16 (02)
[5] Eisentraeger K., ARXIV201009551V1MAT
[6] Subfields of ample fields. Rational maps and definability
Fehm, Arno
[J]. JOURNAL OF ALGEBRA, 2010, 323 (06) : 1738 - 1744
[7] Fried M., 2008, FIELD ARITHMETIC
[8] Large normal extension of Hilbertian fields
Jarden, M
[J]. MATHEMATISCHE ZEITSCHRIFT, 1997, 224 (04) : 555 - 565
[9] DECIDABLE ALGEBRAIC FIELDS
Jarden, Moshe
Shlapentokh, Alexandra
[J]. JOURNAL OF SYMBOLIC LOGIC, 2017, 82 (02) : 474 - 488
[10] Jarden M, 2011, SPRINGER MONOGR MATH, P1, DOI 10.1007/978-3-642-15128-6_1

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