Lindenbaum and Pair Extension Lemma in Infinitary Logics
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00491981" target="_blank" >RIV/67985556:_____/18:00491981 - isvavai.cz</a>
Alternative codes found
RIV/67985807:_____/18:00491981 RIV/00216208:11210/18:10385612
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-662-57669-4_7" target="_blank" >http://dx.doi.org/10.1007/978-3-662-57669-4_7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-662-57669-4_7" target="_blank" >10.1007/978-3-662-57669-4_7</a>
Alternative languages
Result language
angličtina
Original language name
Lindenbaum and Pair Extension Lemma in Infinitary Logics
Original language description
The abstract Lindenbaum lemma is a crucial result in algebraic logic saying that the prime theories form a basis of the closure systems of all theories of an arbitrary given logic. Its usual formulation is however limited to finitary logics, i.e., logics with Hilbert-style axiomatization using finitary rules only. In this contribution, we extend its scope to all logics with a countable axiomatization and a well-behaved disjunction connective. We also relate Lindenbaum lemma to the Pair extension lemma, other well-known result with many applications mainly in the theory of non-classical modal logics. While a restricted form of this lemma (to pairs with finite right-hand side) is, in our context, equivalent to Lindenbaum lemma, we show a perhaps surprising result that in full strength it holds for finitary logics only. Finally we provide examples demonstrating both limitations and applications of our results.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
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
Article name in the collection
Logic, Language, Information and Computation
ISBN
978-3-662-57668-7
ISSN
0302-9743
e-ISSN
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Number of pages
15
Pages from-to
130-144
Publisher name
Springer
Place of publication
Berlin
Event location
Bogotá
Event date
Jul 24, 2018
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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