A consequence of the notional existence of an effectively calculable yet non-recursive function

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dc.contributor.authorOlszewski, Adam
dc.date.accessioned2023-08-10T06:30:38Z
dc.date.available2023-08-10T06:30:38Z
dc.date.issued2021
dc.description.abstractThe present paper is devoted to a discussion of the role of Church’s thesis in setting limits to the cognitive possibilities of mathematics. The specific aim is to analyse the formalized theory of arithmetic as a fundamental mathematical structure related to the theory of computation. By introducing notional non-standard computational abilities into this theory, a non-trivial enlargement of the set of theorems is obtained. The paper also indicates the connection between the inclusion of new functions through the development of axioms and the potential modification of inference rules. In addition, the paper provides an explanation of the role of inclusion of a certain interpretation of the meaning of the axioms of the theory in that theory.en
dc.description.volume53
dc.identifier.doihttps://doi.org/10.15633/acr.5306
dc.identifier.urihttp://hdl.handle.net/123456789/78
dc.language.isoen
dc.publisherUniwersytet Papieski Jana Pawła II w Krakowie
dc.relation.ispartofAnalecta Cracoviensia, 53 (2021), s. 111–139
dc.rightsAttribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.titleA consequence of the notional existence of an effectively calculable yet non-recursive function
dc.title.journalAnalecta Cracoviensia
dc.typearticle
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