Conservative extensions of models of arithmetic.
Two closed categories of filters
Degrees of indeterminacy of games
Prime ideals yield almost maximal ideals
Words, free algebras, and coequalizers
Subgroups of the Baer–Specker group with few endomorphisms but large dual
Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer-Specker group with the following properties. Every endomorphism of G differs from a scalar multiplication by an endomorphism of finite rank. Yet G has uncountably many homomorphisms to ℤ.
Finite Embeddability of Sets and Ultrafilters
A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper we study it in its own right. We also study a related notion of finite embeddability of ultrafilters on the natural numbers. Among other results, we obtain connections between finite embeddability and the algebraic and topological structure of the Stone-Čech...
Homotopy and homology of finite lattices.
Inaccessible cardinals without the axiom of choice
We consider four notions of strong inaccessibility that are equivalent in ZFC and show that they are not equivalent in ZF.
Random orders and gambler's ruin.
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