Definable relations in finite dimensional subspace lattices with involution. Part II: Quantifier-free and homogeneous descriptions

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For finite dimensional hermitean inner product spaces V, over ∗ -fields F, and in the presence of orthogonal bases providing form elements in the prime subfield of F, we show that quantifier-free definable relations in the subspace lattice L(V) , endowed with the involution induced by orthogonality, admit quantifier-free descriptions within F, also in terms of Grassmann–Plücker coordinates. In the latter setting, homogeneous descriptions are obtained if one allows quantification type Σ1 . In absence of involution, these results remain valid.
Publisher
SPRINGER BASEL AG
Issue Date
2019-09
Language
English
Article Type
Article
Citation

ALGEBRA UNIVERSALIS, v.80, no.28, pp.28

ISSN
0002-5240
DOI
10.1007/s00012-019-0603-7
URI
http://hdl.handle.net/10203/263840
Appears in Collection
CS-Journal Papers(저널논문)
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