Distinguishing non-standard natural numbers in a set theory within ?ukasiewicz logic

摘要

In ${mathbf{H}}$ , a set theory with the comprehension principle within ?ukasiewicz infinite-valued predicate logic, we prove that a statement which can be interpreted as “there is an infinite descending sequence of initial segments of ω” is truth value 1 in any model of ${mathbf{H}}$ , and we prove an analogy of Hájek’s theorem with a very simple procedure.