• Corpus ID: 247291906

Games on base matrices

@inproceedings{Fischer2022GamesOB,
  title={Games on base matrices},
  author={Vera Fischer and Marlene Koelbing and Wolfgang Wohofsky},
  year={2022}
}
Using a game characterization of distributivity, we show that base matrices for P(ω)/fin of regular height larger than h necessarily have maximal branches which are not cofinal. 

References

SHOWING 1-10 OF 14 REFERENCES
Tree π-bases for βN − N in various models
On heights of distributivity matrices
We construct a model in which there exists a distributivity matrix of regular height λ larger than h; both λ = c and λ < c are possible. A distributivity matrix is a refining system of mad families
Base matrices of various heights
A classical theorem of Balcar, Pelant, and Simon says that there is a base matrix of height h, where h is the distributivity number of P(ω)/fin. We show that if the continuum c is regular, then there
Order
A model in which the base-matrix tree cannot have cofinal branches
TLDR
A model of ZFC is constructed in which the distributivity cardinal h is , and in which there are no ω 2 -towers in [ ω ] ω so that any base-matrix tree in this model has no cofinal branches.
Games played on Boolean algebras
  • M. Foreman
  • Mathematics
    Journal of Symbolic Logic
  • 1983
TLDR
A partial converse to Jech's theorem is established, namely it gives cardinality conditions on ℬ under which II having a winning strategy implies ω -closure, and considers games of length > ω and generalize Jech’s theorem to these games.
Symbolic Logic
MR. McCOLL still expresses surprise at my declining to answer a Yes or No question which he was pleased to put to me in NATURE (vol. xxiv. p. 124). It was, I should think, almost unique in a
Base Tree Property
TLDR
It is shown that every ρ-closed partial order of size continuum has a base tree and that σ-closed forcing notions of density 𝔠 correspond exactly to regular suborders of the collapsing algebra Coll(ω1, 2ω).
...
...