{"id":"https://openalex.org/W7160532732","doi":"https://doi.org/10.48550/arxiv.2605.05016","title":"Goedel Logics: On the Elimination of The Absoluteness Operator","display_name":"Goedel Logics: On the Elimination of The Absoluteness Operator","publication_year":2026,"publication_date":"2026-05-06","ids":{"openalex":"https://openalex.org/W7160532732","doi":"https://doi.org/10.48550/arxiv.2605.05016"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.05016","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05016","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.05016","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035315045","display_name":"Matthias Baaz","orcid":"https://orcid.org/0000-0002-7815-2501"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Baaz, Matthias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135599347","display_name":"Mariami Gamsakhurdia","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gamsakhurdia, Mariami","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.8712999820709229,"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"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.8712999820709229,"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":0.04659999907016754,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.021900000050663948,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/absoluteness","display_name":"Absoluteness","score":0.9257000088691711},{"id":"https://openalex.org/keywords/g\u00f6dels-incompleteness-theorems","display_name":"G\u00f6del's incompleteness theorems","score":0.6536999940872192},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6276999711990356},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.5763999819755554},{"id":"https://openalex.org/keywords/atomic-formula","display_name":"Atomic formula","score":0.4458000063896179},{"id":"https://openalex.org/keywords/denotation","display_name":"Denotation (semiotics)","score":0.44029998779296875},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.3878999948501587}],"concepts":[{"id":"https://openalex.org/C2780102774","wikidata":"https://www.wikidata.org/wiki/Q4669873","display_name":"Absoluteness","level":2,"score":0.9257000088691711},{"id":"https://openalex.org/C180937797","wikidata":"https://www.wikidata.org/wiki/Q200787","display_name":"G\u00f6del's incompleteness theorems","level":3,"score":0.6536999940872192},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6517000198364258},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6276999711990356},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.5763999819755554},{"id":"https://openalex.org/C203264685","wikidata":"https://www.wikidata.org/wiki/Q2328174","display_name":"Atomic formula","level":2,"score":0.4458000063896179},{"id":"https://openalex.org/C149106765","wikidata":"https://www.wikidata.org/wiki/Q1982453","display_name":"Denotation (semiotics)","level":3,"score":0.44029998779296875},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4027999937534332},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3887999951839447},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.3878999948501587},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.35519999265670776},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.33959999680519104},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3010999858379364},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2759000062942505},{"id":"https://openalex.org/C115633367","wikidata":"https://www.wikidata.org/wiki/Q5254796","display_name":"Delta operator","level":5,"score":0.27239999175071716},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C150355047","wikidata":"https://www.wikidata.org/wiki/Q965432","display_name":"Extensionality","level":2,"score":0.26159998774528503}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.05016","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05016","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.05016","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05016","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"score":0.4199729263782501,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,85],"investigate":[1],"the":[2,5,18,33,46,88,91],"eliminability":[3],"of":[4,67],"absoluteness":[6],"operator":[7],"Delta":[8,13,61],"in":[9,40,90,97],"Goedel":[10],"logics.":[11],"While":[12],"is":[14,62],"not":[15],"definable":[16],"from":[17],"standard":[19],"connectives":[20],"and":[21,76,102],"disrupts":[22],"important":[23],"proof-theoretic":[24],"properties,":[25],"we":[26],"show":[27],"that":[28],"it":[29],"becomes":[30],"eliminable":[31],"at":[32],"propositional":[34,43],"level":[35],"under":[36,109],"a":[37,65,71],"restricted":[38,77],"semantics":[39,78],"which":[41],"all":[42],"atoms":[44],"(except":[45],"truth":[47],"constant":[48],"'True')":[49],"are":[50],"interpreted":[51],"strictly":[52],"below":[53],"1.":[54],"Under":[55],"this":[56],"semantics,":[57],"every":[58],"formula":[59],"containing":[60],"equivalent":[63],"to":[64,100],"disjunction":[66],"chain":[68],"formulas,":[69],"yielding":[70],"Delta-free":[72],"normal":[73],"form":[74],"(standard":[75],"coincide":[79],"w.r.t.":[80],"valid":[81],"formulas":[82],"without":[83],"Delta).":[84],"further":[86],"analyze":[87],"situation":[89],"first-order":[92],"setting,":[93],"where":[94],"Delta-elimination":[95],"fails":[96],"general":[98],"due":[99],"recursion-theoretic":[101],"topological":[103],"constraints,":[104],"but":[105],"can":[106],"be":[107],"recovered":[108],"witnessed":[110],"semantics.":[111]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-08T00:00:00"}
