منابع مشابه
Categorical characterizations of the natural numbers require primitive recursion
Simpson and Yokoyama [Ann. Pure Appl. Logic 164 (2012), 284–293] asked whether there exists a characterization of the natural numbers by a second-order sentence which is provably categorical in the theory RCA0. We answer in the negative, showing that for any characterization of the natural numbers which is provably true in WKL0, the categoricity theorem implies Σ1 induction. On the other hand, ...
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ژورنال
عنوان ژورنال: Journal of Logic and Computation
سال: 2016
ISSN: 0955-792X,1465-363X
DOI: 10.1093/logcom/exw020