Formalizing Ordinal Partition Relations Using Isabelle/HOL
This is an overview of a formalization project in the proof assistant Isabelle/HOL of a number of research results in infinitary combinatorics and set theory (more specifically in ordinal partition relations) by Erdős-Milner, Specker, Larson and Nash-Williams, leading to Larson's proof of the u...
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| Veröffentlicht in: | Experimental mathematics 2022-07, Vol.31 (2), p.383-400 |
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| container_title | Experimental mathematics |
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| creator | Džamonja, Mirna Koutsoukou-Argyraki, Angeliki Paulson, Lawrence C. |
| description | This is an overview of a formalization project in the proof assistant Isabelle/HOL of a number of research results in infinitary combinatorics and set theory (more specifically in ordinal partition relations) by Erdős-Milner, Specker, Larson and Nash-Williams, leading to Larson's proof of the unpublished result by E.C. Milner asserting that for all
,
. This material has been recently formalised by Paulson and is available on the Archive of Formal Proofs; here we discuss some of the most challenging aspects of the formalization process. This project is also a demonstration of working with Zermelo-Fraenkel set theory in higher-order logic. |
| doi_str_mv | 10.1080/10586458.2021.1980464 |
| format | Article |
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,
. This material has been recently formalised by Paulson and is available on the Archive of Formal Proofs; here we discuss some of the most challenging aspects of the formalization process. This project is also a demonstration of working with Zermelo-Fraenkel set theory in higher-order logic.</description><identifier>ISSN: 1058-6458</identifier><identifier>EISSN: 1944-950X</identifier><identifier>DOI: 10.1080/10586458.2021.1980464</identifier><language>eng</language><publisher>Taylor & Francis</publisher><subject>interactive theorem proving ; Isabelle ; Logic ; Mathematics ; Ordinal partition relations ; proof assistants ; set theory</subject><ispartof>Experimental mathematics, 2022-07, Vol.31 (2), p.383-400</ispartof><rights>2021 The Author(s). Published with license by Taylor and Francis Group, LLC 2021</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c391t-6a0f4c23175555f9cbcede49bead5dda3d4944ced7b1b24497697a030f87bec43</citedby><cites>FETCH-LOGICAL-c391t-6a0f4c23175555f9cbcede49bead5dda3d4944ced7b1b24497697a030f87bec43</cites><orcidid>0000-0003-0288-4279 ; 0000-0002-6771-3975 ; 0000-0002-8886-5281</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.tandfonline.com/doi/pdf/10.1080/10586458.2021.1980464$$EPDF$$P50$$Ginformaworld$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.tandfonline.com/doi/full/10.1080/10586458.2021.1980464$$EHTML$$P50$$Ginformaworld$$Hfree_for_read</linktohtml><link.rule.ids>230,314,776,780,881,27901,27902,59620,60409</link.rule.ids><backlink>$$Uhttps://hal.science/hal-03203361$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Džamonja, Mirna</creatorcontrib><creatorcontrib>Koutsoukou-Argyraki, Angeliki</creatorcontrib><creatorcontrib>Paulson, Lawrence C.</creatorcontrib><title>Formalizing Ordinal Partition Relations Using Isabelle/HOL</title><title>Experimental mathematics</title><description>This is an overview of a formalization project in the proof assistant Isabelle/HOL of a number of research results in infinitary combinatorics and set theory (more specifically in ordinal partition relations) by Erdős-Milner, Specker, Larson and Nash-Williams, leading to Larson's proof of the unpublished result by E.C. Milner asserting that for all
,
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,
. This material has been recently formalised by Paulson and is available on the Archive of Formal Proofs; here we discuss some of the most challenging aspects of the formalization process. This project is also a demonstration of working with Zermelo-Fraenkel set theory in higher-order logic.</abstract><pub>Taylor & Francis</pub><doi>10.1080/10586458.2021.1980464</doi><tpages>18</tpages><orcidid>https://orcid.org/0000-0003-0288-4279</orcidid><orcidid>https://orcid.org/0000-0002-6771-3975</orcidid><orcidid>https://orcid.org/0000-0002-8886-5281</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | Experimental mathematics, 2022-07, Vol.31 (2), p.383-400 |
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| language | eng |
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| source | Taylor & Francis Journals Complete |
| subjects | interactive theorem proving Isabelle Logic Mathematics Ordinal partition relations proof assistants set theory |
| title | Formalizing Ordinal Partition Relations Using Isabelle/HOL |
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