Abstract
In \({\mathbf{H}}\), 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 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.
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Yatabe, S. Distinguishing non-standard natural numbers in a set theory within Łukasiewicz logic. Arch. Math. Logic 46, 281–287 (2007). https://doi.org/10.1007/s00153-007-0043-5
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DOI: https://doi.org/10.1007/s00153-007-0043-5