Matches in SemOpenAlex for { <https://semopenalex.org/work/W2498493586> ?p ?o ?g. }
Showing items 1 to 82 of
82
with 100 items per page.
- W2498493586 abstract "In general, two overlapping Boolean algebras always extend to a common Boolean algebra, but three may not. We prove a new sufficient condition for $n$ overlapping Boolean algebras to have a common extension. Combining this with the set-theoretic technique of long $omega_1$-approximation sequences (also known as Davies sequences), we obtain a flexible method of constructing (in ZFC) arbitrarily large Boolean algebras as direct limits of countable Boolean algebras. Along the way, we develop some category theory regarding (co)limits of faces of commutative $n$-cubes and an $n$-ary version of the Interpolation Theorem of propositional logic. Our most elaborate application of the above machinery is a Boolean algebra of size $aleph_n$ with the $n$-ary FN but not the $(n+1)$-ary FN where the $n$-ary FN is a higher-arity variant of the Freese-Nation property. The Stone dual of the $n$-ary FN, $n$-open generation, generalizes Shchepin's concept of openly generated compact spaces. We also show that, given a Boolean algebra $A$ of size $aleph_alpha$ and letting $d=min(alpha+2,omega)$, we have $A$ projective iff it has every $(<d)$-ary FN iff it has a cofinal family of finite subalgebras whose $(<d)$-cube subdiagrams have a strong injectivity property. From this we deduce purely finitary consequences for the Vietoris hyperspace and symmetric power functors in the category of finite discrete spaces and finite functions." @default.
- W2498493586 created "2016-08-23" @default.
- W2498493586 creator A5063863604 @default.
- W2498493586 date "2016-07-27" @default.
- W2498493586 modified "2023-09-27" @default.
- W2498493586 title "Amalgamating many overlapping Boolean algebras" @default.
- W2498493586 cites W1434016993 @default.
- W2498493586 cites W1496446432 @default.
- W2498493586 cites W1964364080 @default.
- W2498493586 cites W1990627365 @default.
- W2498493586 cites W1995912769 @default.
- W2498493586 cites W2023679047 @default.
- W2498493586 cites W2024332480 @default.
- W2498493586 cites W2078046639 @default.
- W2498493586 cites W2114633883 @default.
- W2498493586 cites W2139398339 @default.
- W2498493586 cites W2963203438 @default.
- W2498493586 cites W2963687450 @default.
- W2498493586 cites W3100913861 @default.
- W2498493586 hasPublicationYear "2016" @default.
- W2498493586 type Work @default.
- W2498493586 sameAs 2498493586 @default.
- W2498493586 citedByCount "0" @default.
- W2498493586 crossrefType "posted-content" @default.
- W2498493586 hasAuthorship W2498493586A5063863604 @default.
- W2498493586 hasConcept C10021369 @default.
- W2498493586 hasConcept C110546421 @default.
- W2498493586 hasConcept C114614502 @default.
- W2498493586 hasConcept C118615104 @default.
- W2498493586 hasConcept C136119220 @default.
- W2498493586 hasConcept C14394260 @default.
- W2498493586 hasConcept C156772000 @default.
- W2498493586 hasConcept C188159880 @default.
- W2498493586 hasConcept C202444582 @default.
- W2498493586 hasConcept C207764348 @default.
- W2498493586 hasConcept C2778003309 @default.
- W2498493586 hasConcept C33923547 @default.
- W2498493586 hasConcept C39685927 @default.
- W2498493586 hasConcept C45503250 @default.
- W2498493586 hasConcept C81518389 @default.
- W2498493586 hasConceptScore W2498493586C10021369 @default.
- W2498493586 hasConceptScore W2498493586C110546421 @default.
- W2498493586 hasConceptScore W2498493586C114614502 @default.
- W2498493586 hasConceptScore W2498493586C118615104 @default.
- W2498493586 hasConceptScore W2498493586C136119220 @default.
- W2498493586 hasConceptScore W2498493586C14394260 @default.
- W2498493586 hasConceptScore W2498493586C156772000 @default.
- W2498493586 hasConceptScore W2498493586C188159880 @default.
- W2498493586 hasConceptScore W2498493586C202444582 @default.
- W2498493586 hasConceptScore W2498493586C207764348 @default.
- W2498493586 hasConceptScore W2498493586C2778003309 @default.
- W2498493586 hasConceptScore W2498493586C33923547 @default.
- W2498493586 hasConceptScore W2498493586C39685927 @default.
- W2498493586 hasConceptScore W2498493586C45503250 @default.
- W2498493586 hasConceptScore W2498493586C81518389 @default.
- W2498493586 hasLocation W24984935861 @default.
- W2498493586 hasOpenAccess W2498493586 @default.
- W2498493586 hasPrimaryLocation W24984935861 @default.
- W2498493586 hasRelatedWork W1484594794 @default.
- W2498493586 hasRelatedWork W1702597163 @default.
- W2498493586 hasRelatedWork W1986502338 @default.
- W2498493586 hasRelatedWork W2000174133 @default.
- W2498493586 hasRelatedWork W2005021983 @default.
- W2498493586 hasRelatedWork W2038008480 @default.
- W2498493586 hasRelatedWork W2051531869 @default.
- W2498493586 hasRelatedWork W2063072330 @default.
- W2498493586 hasRelatedWork W2084275485 @default.
- W2498493586 hasRelatedWork W2109600761 @default.
- W2498493586 hasRelatedWork W2168307447 @default.
- W2498493586 hasRelatedWork W2530098671 @default.
- W2498493586 hasRelatedWork W2555814233 @default.
- W2498493586 hasRelatedWork W2593290804 @default.
- W2498493586 hasRelatedWork W27980923 @default.
- W2498493586 hasRelatedWork W2808257774 @default.
- W2498493586 hasRelatedWork W2951697303 @default.
- W2498493586 hasRelatedWork W3099427177 @default.
- W2498493586 hasRelatedWork W2289946635 @default.
- W2498493586 hasRelatedWork W3148239413 @default.
- W2498493586 isParatext "false" @default.
- W2498493586 isRetracted "false" @default.
- W2498493586 magId "2498493586" @default.
- W2498493586 workType "article" @default.