Indifference to symmetry in Hrushovski's ab initio construction

Omer Mermelstein

doi:10.1016/j.apal.2021.103040

Indifference to symmetry in Hrushovski's ab initio construction

Omer Mermelstein

Department of Mathematics

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

Abstract

Denote Hrushovski's non-collapsed ab initio construction for an n-ary relation by M_≁ and the analogous construction for a symmetric n-ary relation by M_∼. We show that M_≁ is isomorphic to a proper reduct of M_∼ and vice versa, and that the combinatorial pregeometries associated with both structures are isomorphic.

Original language	English
Article number	103040
Journal	Annals of Pure and Applied Logic
Volume	173
Issue number	1
DOIs	https://doi.org/10.1016/j.apal.2021.103040
State	Published - 1 Jan 2022

Keywords

Hrushovski construction
Predimension
Pregeometry
Reduct

ASJC Scopus subject areas

Logic

Access to Document

10.1016/j.apal.2021.103040

Cite this

@article{100b57eeda20412a8464df82df16c3b2,

title = "Indifference to symmetry in Hrushovski's ab initio construction",

abstract = "Denote Hrushovski's non-collapsed ab initio construction for an n-ary relation by M≁ and the analogous construction for a symmetric n-ary relation by M∼. We show that M≁ is isomorphic to a proper reduct of M∼ and vice versa, and that the combinatorial pregeometries associated with both structures are isomorphic.",

keywords = "Hrushovski construction, Predimension, Pregeometry, Reduct",

author = "Omer Mermelstein",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2022",

month = jan,

day = "1",

doi = "10.1016/j.apal.2021.103040",

language = "English",

volume = "173",

journal = "Annals of Pure and Applied Logic ",

issn = "0168-0072",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

T1 - Indifference to symmetry in Hrushovski's ab initio construction

AU - Mermelstein, Omer

PY - 2022/1/1

Y1 - 2022/1/1

N2 - Denote Hrushovski's non-collapsed ab initio construction for an n-ary relation by M≁ and the analogous construction for a symmetric n-ary relation by M∼. We show that M≁ is isomorphic to a proper reduct of M∼ and vice versa, and that the combinatorial pregeometries associated with both structures are isomorphic.

AB - Denote Hrushovski's non-collapsed ab initio construction for an n-ary relation by M≁ and the analogous construction for a symmetric n-ary relation by M∼. We show that M≁ is isomorphic to a proper reduct of M∼ and vice versa, and that the combinatorial pregeometries associated with both structures are isomorphic.

KW - Hrushovski construction

KW - Predimension

KW - Pregeometry

KW - Reduct

UR - http://www.scopus.com/inward/record.url?scp=85114764991&partnerID=8YFLogxK

U2 - 10.1016/j.apal.2021.103040

DO - 10.1016/j.apal.2021.103040

M3 - Article

AN - SCOPUS:85114764991

SN - 0168-0072

VL - 173

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 1

M1 - 103040

ER -

Indifference to symmetry in Hrushovski's ab initio construction

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this