Corrigendum to “Unique solutions”

✍ Scribed by Peter Schuster

• Book ID: 102485103
• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 55 KB
• Volume: 53
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200710001

✦ Synopsis

To exclude any unintended interpretation, I need to make more precise some parts of [3], especially of the (complementary) Section 4. First, the name "modulus of uniqueness" was already used in [1]; some history of this concept can also be found in [2, Section 4.1]. Next, WKL is part of the extension of PA ω which occurs in the premiss of the rules proved in [1, Section 4]. 1) Moreover, the rule from [1, Theorem 4.3] corresponds to the implication from FAN to MUN, and thus to the one from FAN to UAM, which is one half of the classification of UAM given in [3, Section 3].

A further matter of concern is the very end of [3, Section 4]. When, in [2, p. 145, second paragraph], a sequence was presented as a means to approximate the solution, the existence of the latter was indeed not at issue. This, however, comes short of giving a true picture of the content of [1, Section 4]: with the two rules from [1, Theorem 4.4, Corollary 4.5], a formal classical proof of the uniqueness of the desired solution is converted into a formal constructive proof of its existence as a continuous function in the parameters. As hinted at before [3, p. 536, lines 10 -14], the idea standing behind [3, Proposition 2.1, Corollary 2.2] can be found in the deductions of these two rules [1, Theorem 4.4, Corollary 4.5] from the aforementioned one [1, Theorem 4.3].