Abstract
The following is a self-contained proof theoretic treatment of two of the principal axiom schemata of current intuitionistic analysis: the axiom of bar induction (Brouwer's bar theorem) and the axiom of continuity. The results are formulated in terms of formal derivability in elementary intuitionistic analysis H(§ 1), so the positive (i.e., derivability) results also apply to elementary classical analysis Z1 (Appendix 1). Both schemata contain the combination of quantifiers νfΛn, where f, g, … are intended to range over free choice sequences of suitable kinds of objects x, y, …; for example, natural numbers or sequences of natural numbers, and n, m, p, r, … over natural numbers (non-negative integers).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
