Model Theory of Projective Spaces

B. A. Berger; A. G. Myasnikov

doi:10.1007/s10469-025-09796-z

Model Theory of Projective Spaces

B. A. Berger
, A. G. Myasnikov

Department of Mathematical Sciences

Stevens Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

It is proved that, for any vector space V over a field f of finite dimension at least 3, the projective space P(V) (the set of all subspaces of V equpped with a binary predicate of inclusion) is regularly injectively bi-interpretable with the field F.

Original language	English
Pages (from-to)	323-348
Number of pages	26
Journal	Algebra and Logic
Volume	63
Issue number	5
DOIs	https://doi.org/10.1007/s10469-025-09796-z
State	Published - Nov 2024

Keywords

bi-interpretation
field
projective geometry
vector space

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title = "Model Theory of Projective Spaces",

abstract = "It is proved that, for any vector space V over a field f of finite dimension at least 3, the projective space P(V) (the set of all subspaces of V equpped with a binary predicate of inclusion) is regularly injectively bi-interpretable with the field F.",

keywords = "bi-interpretation, field, projective geometry, vector space",

author = "Berger, \{B. A.\} and Myasnikov, \{A. G.\}",

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PY - 2024/11

Y1 - 2024/11

N2 - It is proved that, for any vector space V over a field f of finite dimension at least 3, the projective space P(V) (the set of all subspaces of V equpped with a binary predicate of inclusion) is regularly injectively bi-interpretable with the field F.

AB - It is proved that, for any vector space V over a field f of finite dimension at least 3, the projective space P(V) (the set of all subspaces of V equpped with a binary predicate of inclusion) is regularly injectively bi-interpretable with the field F.

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KW - field

KW - projective geometry

KW - vector space

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UR - https://www.scopus.com/pages/publications/105017987883#tab=citedBy

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DO - 10.1007/s10469-025-09796-z

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VL - 63

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EP - 348

JO - Algebra and Logic

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Model Theory of Projective Spaces

Abstract

Keywords

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