Towards Limit Computable Mathematics [chapter]

Susumu Hayashi, Masahiro Nakata
<span title="">2002</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The notion of Limit-Computable Mathematics (LCM) will be introduced. LCM is a fragment of classical mathematics in which the law of excluded middle is restricted to 1 0 2 -formulas. We can give an accountable computational interpretation to the proofs of LCM. The computational content of LCM-proofs is given by Gold's limiting recursive functions, which is the fundamental notion of learning theory. LCM is expected to be a right means for \Proof Animation," which was introduced by the rst author
more &raquo; ... 10]. LCM is related not only to learning theory and recursion theory, but also to many areas in mathematics and computer science such as computational algebra, computability theories in analysis, reverse mathematics, and many others.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45842-5_9">doi:10.1007/3-540-45842-5_9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ajugnuaa5fg5bnx7kfxq7kui2e">fatcat:ajugnuaa5fg5bnx7kfxq7kui2e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190217202049/http://pdfs.semanticscholar.org/06e2/be9b6fcfd40b569bac9b4e10b02f9a99f00d.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/06/e2/06e2be9b6fcfd40b569bac9b4e10b02f9a99f00d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45842-5_9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>