Prime extensions and categoricity in power

Victor Harnik; Jean Pierre Ressayre

doi:10.1007/BF02771568

Prime extensions and categoricity in power

Victor Harnik, Jean Pierre Ressayre

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

Abstract

This paper deals with the notion of prime extension defined by Morley. A connection is established between the categoricity of a theory in a cardinal greater than the power of its language and the existence of prime extensions. For such theories we prove a minimality property of the prime extensions and we conclude by a property of the group of automorphisms of their models.

Original language	English
Pages (from-to)	172-185
Number of pages	14
Journal	Israel Journal of Mathematics
Volume	10
Issue number	2
DOIs	https://doi.org/10.1007/BF02771568
State	Published - Jun 1971
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/BF02771568

Cite this

@article{e5a95bfedfef4f268c1288db9c23c331,

title = "Prime extensions and categoricity in power",

abstract = "This paper deals with the notion of prime extension defined by Morley. A connection is established between the categoricity of a theory in a cardinal greater than the power of its language and the existence of prime extensions. For such theories we prove a minimality property of the prime extensions and we conclude by a property of the group of automorphisms of their models.",

author = "Victor Harnik and Ressayre, {Jean Pierre}",

year = "1971",

month = jun,

doi = "10.1007/BF02771568",

language = "English",

volume = "10",

pages = "172--185",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Prime extensions and categoricity in power

AU - Harnik, Victor

AU - Ressayre, Jean Pierre

PY - 1971/6

Y1 - 1971/6

N2 - This paper deals with the notion of prime extension defined by Morley. A connection is established between the categoricity of a theory in a cardinal greater than the power of its language and the existence of prime extensions. For such theories we prove a minimality property of the prime extensions and we conclude by a property of the group of automorphisms of their models.

AB - This paper deals with the notion of prime extension defined by Morley. A connection is established between the categoricity of a theory in a cardinal greater than the power of its language and the existence of prime extensions. For such theories we prove a minimality property of the prime extensions and we conclude by a property of the group of automorphisms of their models.

UR - http://www.scopus.com/inward/record.url?scp=51649171454&partnerID=8YFLogxK

U2 - 10.1007/BF02771568

DO - 10.1007/BF02771568

M3 - Article

AN - SCOPUS:51649171454

SN - 0021-2172

VL - 10

SP - 172

EP - 185

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -

Prime extensions and categoricity in power

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this