Note on total and partial functions in second-order arithmetic (Proof Theory, Computation Theory and Related Topics)
誠 藤原, 隆 佐藤 · Kyoto University Research Information Repository (Kyoto University) · 2015
We analyze the total and partial extendability for partial functions in second-order arith- metic.In particular, we show that the partial extendability for consistent set of finite partial functions and that for consistent sequence of partial functions are equivalent to WKL (weak K\"onig's lemma) over $RCA_{0}$ , despite the fact that their total extendability derives ACA (arith- metical comprehension).