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We construct several forcing models in each of which there exists a maximal cofinitary group, i.e., a maximal almost disjoint group, G≤Sym(ℕ), such that G is also a maximal almost disjoint family in Sym(ℕ). We also ask several open questions in this area in the fourth section of this paper.
We give a characterization of strongly compact cardinals in terms of Q
λ. We also prove that weakly normal Q-measures on Q
λ are ⊂κ-normal.
In terms of formal deductive systems and multi-dimensional Kripke frames we study logical operations know, informed, common knowledge and common information. Based on  we introduce formal axiomatic systems for common information logics and prove that these systems are sound and complete....
We prove versions of the Dual Ramsey Theorem and the Dual Ellentuck Theorem for families of partitions which are defined in terms of games.
Starting from the definition of `amorphous set' in set theory without the axiom of choice, we propose a notion of rank (which will only make sense for, at most, the class of Dedekind finite sets), which is intended to be an analogue in this situation of Morley rank in model theory.
In this paper we introduce theories of universes in analysis. We discuss a non-uniform, a uniform and a minimal variant. An analysis of the proof-theoretic bounds of these systems is given, using only methods of predicative proof-theory. It turns out that all introduced theories are of...
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