A Logical Framework for Set Theories
Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for Mathematical Knowledge Management. However, in order to be used for...
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2012-03-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1203.6157v1 |
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doaj-084ef5516d8a4261b480d06fd9c5598b |
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Article |
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doaj-084ef5516d8a4261b480d06fd9c5598b2020-11-24T22:55:12ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802012-03-0181Proc. LSFA 201131510.4204/EPTCS.81.1A Logical Framework for Set TheoriesArnon AvronAxiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for Mathematical Knowledge Management. However, in order to be used for this task it is necessary to overcome serious gaps that exist between the "official" formulations of set theory (as given e.g. by formal set theory ZF) and actual mathematical practice. In this work we present a new unified framework for formalizations of axiomatic set theories of different strength, from rudimentary set theory to full ZF. It allows the use of set terms, but provides a static check of their validity.http://arxiv.org/pdf/1203.6157v1 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Arnon Avron |
| spellingShingle |
Arnon Avron A Logical Framework for Set Theories Electronic Proceedings in Theoretical Computer Science |
| author_facet |
Arnon Avron |
| author_sort |
Arnon Avron |
| title |
A Logical Framework for Set Theories |
| title_short |
A Logical Framework for Set Theories |
| title_full |
A Logical Framework for Set Theories |
| title_fullStr |
A Logical Framework for Set Theories |
| title_full_unstemmed |
A Logical Framework for Set Theories |
| title_sort |
logical framework for set theories |
| publisher |
Open Publishing Association |
| series |
Electronic Proceedings in Theoretical Computer Science |
| issn |
2075-2180 |
| publishDate |
2012-03-01 |
| description |
Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for Mathematical Knowledge Management. However, in order to be used for this task it is necessary to overcome serious gaps that exist between the "official" formulations of set theory (as given e.g. by formal set theory ZF) and actual mathematical practice. In this work we present a new unified framework for formalizations of axiomatic set theories of different strength, from rudimentary set theory to full ZF. It allows the use of set terms, but provides a static check of their validity. |
| url |
http://arxiv.org/pdf/1203.6157v1 |
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AT arnonavron alogicalframeworkforsettheories AT arnonavron logicalframeworkforsettheories |
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