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Chapter
Proper Forcing
The aim of this chapter is to develop the theory of proper forcings and their iteration and to provide interesting examples of its usefulness and range of applications. Our presentation is detailed and should ...
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Chapter
Cardinal Arithmetic
Following the work of Gödel and Cohen we now know that it is impossible to determine the exact value of the continuum or of the power set of an arbitrary cardinal. Despite the limitations that the consistency ...
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Article
On Poset Boolean Algebras
Let (P,≤) be a partially ordered set. The poset Boolean algebra of P, denoted F(P), is defined as follows: The set of generators of F(P) is {x p : p∈P}, and the...
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Article
A note on Dilworth's theorem in the infinite case
If ℘ is a poset and every antichain is finite, and if the length of the well-founded poset of antichains is less than ω2 1, then ℘ is the union of countably many chains. We also compute the length of the poset of...