Examples of sets definable by means of two and three quantifiers
Andrzej Włodzimierz Mostowski · Fundamenta Mathematicae · 1955
Publisher Summary There are many categories of mathematical papers. On the one hand, there are first-class papers that are read with interest by many mathematicians and further the development of mathematical thought. On the other hand, there are papers that are studied exclusively by referees appointed for that task by the editors of bibliographical journals and are put aside even by these casual readers. The present chapter belongs to the second category. It has collected a number of very special results that belong to the theory of recursive functions. It considers fractions of the form 10 -x a ( x , y ), where a is a primitive recursive function and also investigates the set of those integers y for which lim 10 -x a ( x , y ) exists and belongs to a preassigned class of real numbers.