König ’ s Theorem

The articles [11], [7], [14], [13], [15], [5], [6], [2], [12], [1], [10], [8], [9], [3], and [4] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: A, B denote ordinal numbers, K, M, N denote cardinal numbers, x, y, z, X , Y , Z, Z1, Z2 denote sets, n denotes a natural number, and f , g denote functions. Let I1 be a function. We say that I1 is cardinal yielding if and only if: (Def. 1) For every x such that x ∈ dom I1 holds I1(x) is a cardinal number.