| bibtype |
J -
Journal Article
|
| ARLID |
0484922 |
| utime |
20240103215400.7 |
| mtime |
20180117235959.9 |
| SCOPUS |
85037378516 |
| WOS |
000450596100001 |
| DOI |
10.1007/s11225-017-9771-7 |
| title
(primary) (eng) |
Extension Properties and Subdirect Representation in Abstract Algebraic Logic |
| specification |
| page_count |
31 s. |
| media_type |
P |
|
| serial |
| ARLID |
cav_un_epca*0292190 |
| ISSN |
0039-3215 |
| title
|
Studia Logica |
| volume_id |
106 |
| volume |
6 (2018) |
| page_num |
1065-1095 |
| publisher |
|
|
| keyword |
Abstract algebraic logic |
| keyword |
Infinitary logics |
| keyword |
Natural extensions |
| keyword |
Natural expansions |
| keyword |
Semilinear logics |
| keyword |
Subdirect representation |
| author
(primary) |
| ARLID |
cav_un_auth*0341114 |
| full_dept (cz) |
Matematická teorie rozhodování |
| full_dept (eng) |
Department of Decision Making Theory |
| department (cz) |
MTR |
| department (eng) |
MTR |
| full_dept |
Department of Decision Making Theory |
| share |
50 |
| name1 |
Lávička |
| name2 |
Tomáš |
| institution |
UTIA-B |
| country |
CZ |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| author
|
| ARLID |
cav_un_auth*0293476 |
| full_dept (cz) |
Matematická teorie rozhodování |
| full_dept |
Department of Decision Making Theory |
| department (cz) |
MTR |
| department |
MTR |
| full_dept |
Department of Decision Making Theory |
| share |
50 |
| name1 |
Noguera |
| name2 |
Carles |
| institution |
UTIA-B |
| garant |
A |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| source |
|
| cas_special |
| project |
| ARLID |
cav_un_auth*0349495 |
| project_id |
GA17-04630S |
| agency |
GA ČR |
|
| abstract
(eng) |
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. |
| RIV |
BA |
| FORD0 |
10000 |
| FORD1 |
10100 |
| FORD2 |
10101 |
| reportyear |
2019 |
| num_of_auth |
2 |
| inst_support |
RVO:67985556 |
| permalink |
http://hdl.handle.net/11104/0280148 |
| confidential |
S |
| mrcbC86 |
3+4 Article Mathematics|Logic|Philosophy |
| mrcbT16-e |
LOGIC|MATHEMATICS |
| mrcbT16-j |
0.393 |
| mrcbT16-s |
0.474 |
| mrcbT16-B |
30.582 |
| mrcbT16-D |
Q3 |
| mrcbT16-E |
Q3 |
| arlyear |
2018 |
| mrcbU14 |
85037378516 SCOPUS |
| mrcbU24 |
PUBMED |
| mrcbU34 |
000450596100001 WOS |
| mrcbU63 |
cav_un_epca*0292190 Studia Logica 0039-3215 1572-8730 Roč. 106 č. 6 2018 1065 1095 Springer |
|