Extension Properties and Subdirect Representation in Abstract Algebraic Logic
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00484922" target="_blank" >RIV/67985556:_____/18:00484922 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11225-017-9771-7" target="_blank" >http://dx.doi.org/10.1007/s11225-017-9771-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11225-017-9771-7" target="_blank" >10.1007/s11225-017-9771-7</a>
Alternative languages
Result language
angličtina
Original language name
Extension Properties and Subdirect Representation in Abstract Algebraic Logic
Original language description
This paper continues the investigation, started in Lávička and Noguera (Stud Log 105(3): 521–551, 2017), of infinitary propositional logics from the perspective of their algebraic completeness and filter extension properties in abstract algebraic logic. If follows from the Lindenbaum Lemma used in standard proofs of algebraic completeness that, in every finitary logic, (completely) intersection-prime theories form a basis of the closure system of all theories. In this article we consider the open problem of whether these properties can be transferred to lattices of filters over arbitrary algebras of the logic. We show that in general the answer is negative, obtaining a richer hierarchy of pairwise different classes of infinitary logics that we separate with natural examples. As by-products we obtain a characterization of subdirect representation for arbitrary logics, develop a fruitful new notion of natural expansion, and contribute to the understanding of semilinear logics.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-04630S" target="_blank" >GA17-04630S: Predicate graded logics and their applications to computer science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Studia Logica
ISSN
0039-3215
e-ISSN
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Volume of the periodical
106
Issue of the periodical within the volume
6
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
31
Pages from-to
1065-1095
UT code for WoS article
000450596100001
EID of the result in the Scopus database
2-s2.0-85037378516