A. Pelc, Solution of a problem of Ulam on countable sequences of sets,
*Fundamenta Mathematicae* 114 (1981), pp. 113-118.

Abstract:

Let *E* be a set of cardinality continuum and
*{A _{n}: n natural}* an arbitrary sequence of subsets of

A. Pelc, Ideals on the real line and Ulam's problem,
*Fundamenta Mathematicae* 112 (1981), pp. 165-170.

Abstract:

We prove that the union of a countable family of continuum-complete fields of subsets of the reals, each of which contains all singletons but not all sets of reals, cannot contain all sets of reals.

A. Pelc, Invariant measures on commutative semigroups, Proc. "Open Days in Model Theory and Set Theory", Jadwisin, Poland, September 1981, pp. 249-258.

Abstract:

Our main result is the following: Assume that *(S,+)* is a commutative,
cancellative semigroup with unity, whose cardinality is greater or
equal than a real-valued measurable cardinal. Then there exists a universal
semiregular invariant measure on *S*.