Special square sequences

Weak Square Sequences and Special Aronszajn Trees

A classical theorem of set theory is the equivalence of the weak square principle μ with the existence of a special Aronszajn tree on μ +. We introduce the notion of a weak square sequence on any regular uncountable cardinal, and prove that the equivalence between weak square sequences and special Aronszajn trees holds in general. Recall the weak square principle μ for an infinite cardinal μ, w...

Reconstructions of Special Sequences

We discuss here some methods for reconstructing special sequences which generate special polygonal arcs in E T. For such reconstructions we introduce a ”mid” function which cuts out the middle part of a sequence; the ”⇃” function, which cuts down the left part of a sequence at some point; the ”⇂” function for cutting down the right part at some point; and the ”⇃⇂” function for cutting down both...

More fine structural global square sequences

Global square sequences in extender models

Square products of punctured sequences of factorials

The following problem is solved: for a positive integer n, for what m is ( ∏n k=1 k!)/m! a perfect square (1 ≤ m ≤ n)? The following appeared in Puzzle Corner 11 [7, p. 13] of a recent issue of this Gazette. Factorial fun The numbers 1!, 2!, 3!, . . . , 100! are written on a blackboard. Is it possible to erase one of the numbers so that the product of the remaining 99 numbers is a perfect squar...