Currently displaying 1 – 9 of 9

Showing per page

Order by Relevance | Title | Year of publication

Embedding partially ordered sets into ω ω

Ilijas Farah — 1996

Fundamenta Mathematicae

We investigate some natural questions about the class of posets which can be embedded into ⟨ω,≤*⟩. Our main tool is a simple ccc forcing notion H E which generically embeds a given poset E into ⟨ω,≤*⟩ and does this in a “minimal” way (see Theorems 9.1, 10.1, 6.1 and 9.2).

OCA and towers in 𝒫 ( ) / f i n

Ilijas Farah — 1996

Commentationes Mathematicae Universitatis Carolinae

We shall show that Open Coloring Axiom has different influence on the algebra 𝒫 ( ) / f i n than on / f i n . The tool used to accomplish this is forcing with a Suslin tree.

Is 𝓟(ω) a subalgebra?

Alan DowIlijas Farah — 2004

Fundamenta Mathematicae

We consider the question of whether 𝒫(ω) is a subalgebra whenever it is a quotient of a Boolean algebra by a countably generated ideal. This question was raised privately by Murray Bell. We obtain two partial answers under the open coloring axiom. Topologically our first result is that if a zero-dimensional compact space has a zero-set mapping onto βℕ, then it has a regular closed zero-set mapping onto βℕ. The second result is that if the compact space has density at most ω₁, then it will map onto...

Existentially closed II₁ factors

Ilijas FarahIsaac GoldbringBradd HartDavid Sherman — 2016

Fundamenta Mathematicae

We examine the properties of existentially closed ( ω -embeddable) II₁ factors. In particular, we use the fact that every automorphism of an existentially closed ( ω -embeddable) II₁ factor is approximately inner to prove that Th() is not model-complete. We also show that Th() is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonisomorphic existentially closed models of Th().

Page 1

Download Results (CSV)