Name
Abstract | ||
|---|---|---|
A Souslin algebra is a complete Boolean algebra whose main features are ruled by a tight combination of an antichain condition with an infinite distributive law. The present article divides into two parts. In the first part a representation theory for the complete and atomless subalgebras of Souslin algebras is established (building on ideas of Jech and Jensen). With this we obtain some basic results on the possible types of subalgebras and their interrelation. The second part begins with a review of some generalizations of results from descriptive set theory concerning Baire category which are then used in non-trivial Souslin tree constructions that yield Souslin algebras with a remarkable subalgebra structure. In particular, we use this method to prove that under the diamond principle there is a bi-embeddable though not isomorphic pair of homogeneous Souslin algebras. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1007/s00153-010-0202-y | Arch. Math. Log. |
Keywords | Field | DocType |
complete boolean algebra,baire category.,atomless subalgebras,. souslin algebra,souslin algebra embeddings,basic result,diamond principle,representation theory,antichain condition,souslin algebra,souslin tree,homogeneous souslin algebra,non-trivial souslin tree construction,descriptive set theory,baire category,boolean algebra,distributive law | Subalgebra,Distributive property,Discrete mathematics,Combinatorics,Antichain,Algebra,Baire space,Representation theory,Descriptive set theory,Diamond principle,Complete Boolean algebra,Mathematics | Journal |
Volume | Issue | ISSN |
50 | 1-2 | 1432-0665 |
Citations | PageRank | References |
0 | 0.34 | 5 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gido Scharfenberger-Fabian | 1 | 2 | 1.44 |