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Logics and admissible rules of constructive set theories

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type , Preprint 10 Apr 2023Embargo end date: 01 Jan 2022 English Publisher:The Royal SocietyJournal:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, volume 381 (issn: 1364-503X, eissn: 1471-2962, Copyright policy )Funded by:NWO | Optimal Proofs, EC | MOSAIC
Authors: Rosalie Iemhoff; Robert Passmann;

doi: 10.1098/rsta.2022.0018 , 10.48550/arxiv.2212.03105

pmid: 37031696

pmc: PMC10083100

arXiv: 2212.03105

Logics and admissible rules of constructive set theories

Abstract

We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We finally provide examples of a number of set theories that are extensible. This article is part of the theme issue ‘Modern perspectives in Proof Theory’.

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Keywords

logic, admissible rules, substitution, FOS: Mathematics, constructive set theory, extensible theories, Mathematics - Logic, Articles, Logic (math.LO)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green
hybrid
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