Distinguishing non-standard natural numbers in a set theory within Łukasiewicz logic. (English) Zbl 1110.03049

Summary: In \(\mathbb{H}\), a set theory with the comprehension principle within Łukasiewicz infinite-valued predicate logic, we prove that a statement which can be interpreted as “there is an infinite descending sequence of initial segments of \(\omega\)” has truth value 1 in any model of \(\mathbb{H}\), and we prove an analogy of Hájek’s theorem [ibid. 44, No. 6, 763–782 (2005; Zbl 1096.03064)] with a very simple procedure.


03E72 Theory of fuzzy sets, etc.
03B52 Fuzzy logic; logic of vagueness
03B50 Many-valued logic


Zbl 1096.03064
Full Text: DOI


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