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Preservation theorems on finite structures

Technical Report:

Abstract

This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ``homomorphism into`` case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs.
Authors:
Publication Date:
Sep 01, 1994
Product Type:
Technical Report
Report Number:
IC-94/273
Reference Number:
SCA: 661300; PA: AIX-26:012318; EDB-95:032009; SN: 95001324704
Resource Relation:
Other Information: PBD: Sep 1994
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MATHEMATICAL LOGIC; INTERPOLATION; MATHEMATICAL MODELS; 661300; OTHER ASPECTS OF PHYSICAL SCIENCE
OSTI ID:
10112438
Research Organizations:
International Centre for Theoretical Physics (ICTP), Trieste (Italy)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ON: DE95613442; TRN: XA9438395012318
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
7 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Hebert, M. Preservation theorems on finite structures. IAEA: N. p., 1994. Web.
Hebert, M. Preservation theorems on finite structures. IAEA.
Hebert, M. 1994. "Preservation theorems on finite structures." IAEA.
@misc{etde_10112438,
title = {Preservation theorems on finite structures}
author = {Hebert, M}
abstractNote = {This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ``homomorphism into`` case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs.}
place = {IAEA}
year = {1994}
month = {Sep}
}