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Article
More results in polychromatic Ramsey theory
We study polychromatic Ramsey theory with a focus on colourings of [ω 2]2. We show that in the absence of GCH there is a wide range of possibilities. In particular each of the following is consist...
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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
Poset algebras over well quasi-ordered posets
A new class of partial order-types, class \({\mathcal{G}}^{+}_{bqo}\) is defined and investigated here. A poset P is ...
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Article
Infinite games on finite sets
We study a family of infinite games with imperfect information introduced by B. Model for two players that alternately remove and add points to a finite set. We investigate the existence of imperfect informati...
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Article
On Jakovlev spaces
A topological spaceX is called weakly first countable, if for every pointx there is a countable family {C n x |n ∈ω} such thatx ∈C ...
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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
On a superatomic Boolean algebra which is not generated by a well-founded sublattice
Let b denote the unboundedness number of ωω. That is, b is the smallest cardinality of a subset \(F \subseteq \omega ^\omega \) ...
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Article
Martin's axiom and \(\Delta^2_1\) well-ordering of the reals
Assuming an inaccessible cardinal \(\kappa\) , there is a generic extension in which \(MA + 2^{\aleph_0} = \kappa\) holds and the reals have a
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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...
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Article
Initial segments of the degrees of size ℵ1
We settle a series of questions first raised by Yates at the Jerusalem (1968) Colloquium on Mathematical Logic by characterizing the initial segments of the degrees of unsolvability of size ℵ1: Every upper semi-l...