THE DEFINABLE (P, Q)-THEOREM FOR DISTAL THEORIES

被引:4
作者
Boxall, Gareth [1 ]
Kestner, Charlotte [2 ]
机构
[1] Stellenbosch Univ, Dept Math Sci, ZA-7600 Stellenbosch, South Africa
[2] Univ Cent Lancashire, Dept Phys Sci & Comp, Jeremiah Horrocks Inst Math Phys & Astron, Fylde Rd, Preston PR1 2HE, Lancs, England
关键词
definable; (p; q); distality; forking; NIP; FORKING;
D O I
10.1017/jsl.2016.72
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Answering a special case of a question of Chernikov and Simon, we show that any nondividing formula over a model M in a distal NIP theory is a member of a consistent definable family, definable over M.
引用
收藏
页码:123 / 127
页数:5
相关论文
共 8 条
[1]   EXTERNALLY DEFINABLE SETS AND DEPENDENT PAIRS II [J].
Chernikov, Artem ;
Simon, Pierre .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 367 (07) :5217-5235
[2]   FORKING AND DIVIDING IN NTP2 THEORIES [J].
Chernikov, Artem ;
Kaplan, Itay .
JOURNAL OF SYMBOLIC LOGIC, 2012, 77 (01) :1-20
[3]   Dependent first order theories, continued [J].
Shelah, Saharon .
ISRAEL JOURNAL OF MATHEMATICS, 2009, 173 (01) :1-60
[4]   Invariant types in NIP theories [J].
Simon, Pierre .
JOURNAL OF MATHEMATICAL LOGIC, 2015, 15 (02)
[5]   ON FORKING AND DEFINABILITY OF TYPES IN SOME DP-MINIMAL THEORIES [J].
Simon, Pierre ;
Starchenko, Sergei .
JOURNAL OF SYMBOLIC LOGIC, 2014, 79 (04) :1020-1024
[6]   DP-MINIMALITY: INVARIANT TYPES AND DP-RANK [J].
Simon, Pierre .
JOURNAL OF SYMBOLIC LOGIC, 2014, 79 (04) :1025-1045
[7]   Distal and non-distal NIP theories [J].
Simon, Pierre .
ANNALS OF PURE AND APPLIED LOGIC, 2013, 164 (03) :294-318
[8]  
Simon Pierre, 2015, A Guide to NIP Theories