Annals of Pure and Applied Logic 66 (2):113-162 (1994)

C-minimality is a variant of o-minimality in which structures carry, instead of a linear ordering, a ternary relation interpretable in a natural way on set of maximal chains of a tree. This notion is discussed, a cell-decomposition theorem for C-minimal structures is proved, and a notion of dimension is introduced. It is shown that C-minimal fields are precisely valued algebraically closed fields. It is also shown that, if certain specific ‘bad’ functions are not definable, then algebraic closure has the exchange property, and for definable sets dimension coincides with the rank obtained from algebraic closure
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/0168-0072(94)90064-7
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 70,214
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

On Variants of o-Minimality.Dugald Macpherson & Charles Steinhorn - 1996 - Annals of Pure and Applied Logic 79 (2):165-209.
More on Definable Sets of P-Adic Numbers.Philip Scowcroft - 1988 - Journal of Symbolic Logic 53 (3):912-920.

Add more references

Citations of this work BETA

A Version of o-Minimality for the P-Adics.Deirdre Haskell & Dugald Macpherson - 1997 - Journal of Symbolic Logic 62 (4):1075-1092.
On Variants of o-Minimality.Dugald Macpherson & Charles Steinhorn - 1996 - Annals of Pure and Applied Logic 79 (2):165-209.
B-Minimality.Raf Cluckers & François Loeser - 2007 - Journal of Mathematical Logic 7 (2):195-227.

View all 23 citations / Add more citations

Similar books and articles

Definable Open Sets As Finite Unions of Definable Open Cells.Simon Andrews - 2010 - Notre Dame Journal of Formal Logic 51 (2):247-251.
A Note on Weakly O-Minimal Structures and Definable Completeness.Alfred Dolich - 2007 - Notre Dame Journal of Formal Logic 48 (2):281-292.
On Dp-Minimal Ordered Structures.Pierre Simon - 2011 - Journal of Symbolic Logic 76 (2):448 - 460.
Presburger Sets and P-Minimal Fields.Raf Cluckers - 2003 - Journal of Symbolic Logic 68 (1):153-162.
Lattice Ordered O -Minimal Structures.Carlo Toffalori - 1998 - Notre Dame Journal of Formal Logic 39 (4):447-463.
On Minimal Structures.Oleg V. Belegradek - 1998 - Journal of Symbolic Logic 63 (2):421-426.
Quasi-o-Minimal Structures.Oleg Belegradek, Ya'acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.


Added to PP index

Total views
16 ( #665,797 of 2,507,559 )

Recent downloads (6 months)
2 ( #277,263 of 2,507,559 )

How can I increase my downloads?


My notes