Header

UZH-Logo

Maintenance Infos

Generalized prime models


Fittler, Robert (1971). Generalized prime models. Journal of Symbolic Logic, 36(4):593-606.

Abstract

A prime model <jats:italic>O</jats:italic> of some complete theory <jats:italic>T</jats:italic> is a model which can be elementarily imbedded into any model of <jats:italic>T</jats:italic> (cf. Vaught [7, Introduction]). We are going to replace the assumption that <jats:italic>T</jats:italic> is complete and that the maps between the models of <jats:italic>T</jats:italic> are elementary imbeddings (elementary extensions) by more general conditions. <jats:italic>T</jats:italic> will always be a first order theory with identity and may have function symbols. The language <jats:italic>L(T)</jats:italic> of <jats:italic>T</jats:italic> will be denumerable. The maps between models will be so called <jats:italic>F</jats:italic>-maps, i.e. maps which preserve a certain set <jats:italic>F</jats:italic> of formulas of <jats:italic>L(T)</jats:italic> (cf. I.1, 2). Roughly speaking a generalized prime model of <jats:italic>T</jats:italic> is a denumerable model <jats:italic>O</jats:italic> which permits an <jats:italic>F</jats:italic>-map <jats:italic>O→M</jats:italic> into any model <jats:italic>M</jats:italic> of <jats:italic>T</jats:italic>. Furthermore <jats:italic>O</jats:italic> has to be “generated” by formulas which belong to a certain subset <jats:italic>G</jats:italic> of <jats:italic>F</jats:italic>.

Abstract

A prime model <jats:italic>O</jats:italic> of some complete theory <jats:italic>T</jats:italic> is a model which can be elementarily imbedded into any model of <jats:italic>T</jats:italic> (cf. Vaught [7, Introduction]). We are going to replace the assumption that <jats:italic>T</jats:italic> is complete and that the maps between the models of <jats:italic>T</jats:italic> are elementary imbeddings (elementary extensions) by more general conditions. <jats:italic>T</jats:italic> will always be a first order theory with identity and may have function symbols. The language <jats:italic>L(T)</jats:italic> of <jats:italic>T</jats:italic> will be denumerable. The maps between models will be so called <jats:italic>F</jats:italic>-maps, i.e. maps which preserve a certain set <jats:italic>F</jats:italic> of formulas of <jats:italic>L(T)</jats:italic> (cf. I.1, 2). Roughly speaking a generalized prime model of <jats:italic>T</jats:italic> is a denumerable model <jats:italic>O</jats:italic> which permits an <jats:italic>F</jats:italic>-map <jats:italic>O→M</jats:italic> into any model <jats:italic>M</jats:italic> of <jats:italic>T</jats:italic>. Furthermore <jats:italic>O</jats:italic> has to be “generated” by formulas which belong to a certain subset <jats:italic>G</jats:italic> of <jats:italic>F</jats:italic>.

Statistics

Citations

Dimensions.ai Metrics

Altmetrics

Downloads

15 downloads since deposited on 10 Oct 2018
7 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Language:English
Date:1 December 1971
Deposited On:10 Oct 2018 13:40
Last Modified:31 Jul 2020 01:57
Publisher:Association for Symbolic Logic (ASL)
ISSN:0022-4812
OA Status:Green
Publisher DOI:https://doi.org/10.2307/2272463
Related URLs:https://www.swissbib.ch/Search/Results?lookfor=nationallicencecambridge1023072272463 (Library Catalogue)

Download

Green Open Access

Download PDF  'Generalized prime models'.
Preview
Content: Published Version
Language: English
Filetype: PDF (Nationallizenz 142-005)
Size: 911kB
View at publisher