Cardinal characteristics associated with families of functions and permutations

Abstract

The Continuum Hypothesis (CH) states that the size of the set of real numbers c is the least uncountable cardinal, i.e. c = N₁. In the absence of CH, it is possible that there are cardinals that lie between N₁ and c. Many of them are cardinals of infinite families related to some concepts in infinite combinatorics, called cardinal characteristics. Most of these cardinals are defined on families of infinite sets of natural numbers. We study families of functions and permutations on the set of natural numbers with some combinatorial properties and associated cardinal characteristics. We give relations among these cardinals and other well-known ones as well as related consistency results.