{"id":"https://openalex.org/W7148848883","doi":"https://doi.org/10.1007/s11786-025-00624-2","title":"On the Theory of Order Over Real Numbers","display_name":"On the Theory of Order Over Real Numbers","publication_year":2026,"publication_date":"2026-04-03","ids":{"openalex":"https://openalex.org/W7148848883","doi":"https://doi.org/10.1007/s11786-025-00624-2"},"language":"en","primary_location":{"id":"doi:10.1007/s11786-025-00624-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11786-025-00624-2","pdf_url":null,"source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078094550","display_name":"Bernard Boigelot","orcid":"https://orcid.org/0009-0009-4721-3824"},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Bernard Boigelot","raw_affiliation_strings":["Montefiore Institute, B28, University of Li\u00e8ge, 4000, Li\u00e8ge, Belgium"],"raw_orcid":"https://orcid.org/0009-0009-4721-3824","affiliations":[{"raw_affiliation_string":"Montefiore Institute, B28, University of Li\u00e8ge, 4000, Li\u00e8ge, Belgium","institution_ids":["https://openalex.org/I157674565"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Pascal Fontaine","orcid":"https://orcid.org/0000-0003-4700-6031"},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Pascal Fontaine","raw_affiliation_strings":["Montefiore Institute, B28, University of Li\u00e8ge, 4000, Li\u00e8ge, Belgium"],"raw_orcid":"https://orcid.org/0000-0003-4700-6031","affiliations":[{"raw_affiliation_string":"Montefiore Institute, B28, University of Li\u00e8ge, 4000, Li\u00e8ge, Belgium","institution_ids":["https://openalex.org/I157674565"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5132903750","display_name":"Baptiste Vergain","orcid":null},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Baptiste Vergain","raw_affiliation_strings":["Montefiore Institute, B28, University of Li\u00e8ge, 4000, Li\u00e8ge, Belgium"],"raw_orcid":"https://orcid.org/0009-0003-5545-4579","affiliations":[{"raw_affiliation_string":"Montefiore Institute, B28, University of Li\u00e8ge, 4000, Li\u00e8ge, Belgium","institution_ids":["https://openalex.org/I157674565"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078094550","https://openalex.org/A5132903750"],"corresponding_institution_ids":["https://openalex.org/I157674565"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.7961485,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.43140000104904175,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.43140000104904175,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.25429999828338623,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.2538999915122986,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.8086000084877014},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6378999948501587},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.6035000085830688},{"id":"https://openalex.org/keywords/monadic-predicate-calculus","display_name":"Monadic predicate calculus","score":0.5733000040054321},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5170000195503235},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.47200000286102295},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.4101000130176544},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4097000062465668},{"id":"https://openalex.org/keywords/model-theory","display_name":"Model theory","score":0.4088999927043915}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8086000084877014},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6378999948501587},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6171000003814697},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.6035000085830688},{"id":"https://openalex.org/C124656256","wikidata":"https://www.wikidata.org/wiki/Q6897882","display_name":"Monadic predicate calculus","level":4,"score":0.5733000040054321},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5170000195503235},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.47200000286102295},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.4101000130176544},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4097000062465668},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.4088999927043915},{"id":"https://openalex.org/C144791301","wikidata":"https://www.wikidata.org/wiki/Q1548746","display_name":"Second-order logic","level":4,"score":0.4066999852657318},{"id":"https://openalex.org/C4777664","wikidata":"https://www.wikidata.org/wiki/Q1536492","display_name":"Linear temporal logic","level":2,"score":0.38960000872612},{"id":"https://openalex.org/C25016198","wikidata":"https://www.wikidata.org/wiki/Q781833","display_name":"Temporal logic","level":2,"score":0.3873000144958496},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3707999885082245},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.3246999979019165},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31679999828338623},{"id":"https://openalex.org/C28901747","wikidata":"https://www.wikidata.org/wiki/Q177571","display_name":"Decision theory","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C16221470","wikidata":"https://www.wikidata.org/wiki/Q846564","display_name":"Conjunctive normal form","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C47884741","wikidata":"https://www.wikidata.org/wiki/Q1166618","display_name":"Mathematical logic","level":2,"score":0.3003000020980835},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C203264685","wikidata":"https://www.wikidata.org/wiki/Q2328174","display_name":"Atomic formula","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27790001034736633},{"id":"https://openalex.org/C23123167","wikidata":"https://www.wikidata.org/wiki/Q7661193","display_name":"Symbolic trajectory evaluation","level":3,"score":0.27410000562667847},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C161445131","wikidata":"https://www.wikidata.org/wiki/Q4669950","display_name":"Abstract model theory","level":5,"score":0.27230000495910645},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2621000111103058},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.2563999891281128}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11786-025-00624-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11786-025-00624-2","pdf_url":null,"source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8132250905036926}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1496394707","https://openalex.org/W1555138513","https://openalex.org/W1580868918","https://openalex.org/W1956775607","https://openalex.org/W1979919662","https://openalex.org/W2031528374","https://openalex.org/W2036472753","https://openalex.org/W2046306944","https://openalex.org/W2056871658","https://openalex.org/W2062792526","https://openalex.org/W2095689360","https://openalex.org/W2157319504","https://openalex.org/W2173684246","https://openalex.org/W2598159508","https://openalex.org/W4244088669","https://openalex.org/W4385701322","https://openalex.org/W4400973331","https://openalex.org/W4402145840"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-05T06:14:27.290980","created_date":"2026-04-04T00:00:00"}