Working with Hardy hierarchy and the notion of largeness determined by it, we define the notion of a partition of a finite set of natural numbers $A=∪_{i
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Continuing the earlier research [Fund. Math. 129 (1988) and 149 (1996)] we give some information about extending automorphisms of models of PA to cofinal extensions.
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We prove a version of the Ramsey theorem for partitions of (increasing) n-tuples. We derive this result from a version of König's infinity lemma for ξ-large trees. Here ξ < ε₀ and the notion of largeness is in the sense of Hardy hierarchy.
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We continue the earlier research of [1]. In particular, we work out a class of regular interstices and show that selective types are realized in regular interstices. We also show that, contrary to the situation above definable elements, the stabilizer of an element inside M(0) whose type is selective need not be maximal.
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