Extension Properties and Subdirect Representation in Abstract Algebraic Logic

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Extension Properties and Subdirect Representation in Abstract Algebraic Logic

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Extension Properties and Subdirect Representation in Abstract Algebraic Logic

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA17-04630S" target="_blank" >GA17-04630S: Predikátové škálované logiky a jejich aplikace v informatice</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Studia Logica

ISSN

0039-3215

e-ISSN

—

Svazek periodika

106

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

31

Strana od-do

1065-1095

Kód UT WoS článku

000450596100001

EID výsledku v databázi Scopus

2-s2.0-85037378516