zbMATH — the first resource for mathematics

Morley degree in unidimensional compact complex spaces. (English) Zbl 1100.03029
Summary: Let \({\mathcal A}\) be the category of all reduced compact complex spaces, viewed as a multi-sorted first-order structure, in the standard way. Let \({\mathcal U}\) be a sub-category of \({\mathcal A}\), which is closed under the taking of products and analytic subsets, and whose morphisms include the projections. Under the assumption that \(\text{Th} ({\mathcal U})\) is unidimensional, we show that Morley rank is equal to Noetherian dimension, in any elementary extension of \({\mathcal U}\). As a result, we are able to show that Morley degree is definable in \(\text{Th}({\mathcal U})\), when \(\text{Th}({\mathcal U})\) is unidimensional.
03C65 Models of other mathematical theories
32C15 Complex spaces
Full Text: DOI
[1] Coherent analytic sheaves 265 (1984) · Zbl 0537.32001
[2] DOI: 10.1007/BF02808211 · Zbl 0773.12005
[3] Memorias de Matemática del Instituto Jorge Juan, Madrid 30 (1977)
[4] Uncountably categorical theories 117 (1993)
[5] Classification theory (revised edition) 92 (1990)
[6] A definability result for compact complex spaces 691 pp 241– (2004)
[7] DOI: 10.1090/S0002-9947-03-03383-X · Zbl 1021.03025
[8] Compact complex manifolds with the DOP and other properties 67 pp 737– (2002) · Zbl 1005.03040
[9] On Lascar rank and Morley rank of definable groups in differentially closed fields 67 pp 1189– (2002) · Zbl 1018.03034
[10] Workshop on Hubert’s Tenth Problem: Relations with arithmetic and algebraic geometry 270 pp 323– (2000)
[11] Journal für die reine und angewandte Mathematik (2003)
[12] Logic colloquium ’01 20 pp 317– (2005)
[13] Seminaire F. Norguet, vol. 111 (1978)
[14] Stability in model theory 36 (1987)
[15] DOI: 10.1090/S0894-0347-96-00180-4 · Zbl 0843.03020
[16] Several complex variables VII 74 (1994)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.