{"id":"https://openalex.org/W2024020693","doi":"https://doi.org/10.1002/malq.200410035","title":"Worms, gaps, and hydras","display_name":"Worms, gaps, and hydras","publication_year":2005,"publication_date":"2005-06-08","ids":{"openalex":"https://openalex.org/W2024020693","doi":"https://doi.org/10.1002/malq.200410035","mag":"2024020693"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200410035","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410035","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"MLQ","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/A5038321878","display_name":"Lorenzo Carlucci","orcid":"https://orcid.org/0000-0001-8238-0315"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]},{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["IT","US"],"is_corresponding":true,"raw_author_name":"Lorenzo Carlucci","raw_affiliation_strings":["Universita\u0300 di Siena, Dipartimento di Matematica, Pian dei Mantellini 44, 00153, Siena, Italy","University of Delaware, Department of Computer and Information Sciences, Newark, DE 19716, USA","Universit\u00e0 di Siena, Dipartimento di Matematica, Pian dei Mantellini 44, 00153, Siena, Italy"],"affiliations":[{"raw_affiliation_string":"Universita\u0300 di Siena, Dipartimento di Matematica, Pian dei Mantellini 44, 00153, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]},{"raw_affiliation_string":"University of Delaware, Department of Computer and Information Sciences, Newark, DE 19716, USA","institution_ids":["https://openalex.org/I86501945"]},{"raw_affiliation_string":"Universit\u00e0 di Siena, Dipartimento di Matematica, Pian dei Mantellini 44, 00153, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038321878"],"corresponding_institution_ids":["https://openalex.org/I102064193","https://openalex.org/I86501945"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":1.3465,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.81335189,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"51","issue":"4","first_page":"342","last_page":"350"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9879999756813049,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9879999756813049,"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":0.970300018787384,"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/T11567","display_name":"semigroups and automata theory","score":0.9445000290870667,"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/sequence","display_name":"Sequence (biology)","score":0.6988730430603027},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.696043074131012},{"id":"https://openalex.org/keywords/lernaean-hydra","display_name":"Lernaean Hydra","score":0.513624370098114},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.478056937456131},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.427074670791626},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3978303372859955},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3717525005340576},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3318224549293518},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.08823820948600769}],"concepts":[{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6988730430603027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.696043074131012},{"id":"https://openalex.org/C34781881","wikidata":"https://www.wikidata.org/wiki/Q170379","display_name":"Lernaean Hydra","level":2,"score":0.513624370098114},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.478056937456131},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.427074670791626},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3978303372859955},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3717525005340576},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3318224549293518},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.08823820948600769},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C95444343","wikidata":"https://www.wikidata.org/wiki/Q7141","display_name":"Cell biology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/malq.200410035","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410035","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"MLQ","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.94.3417","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.94.3417","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cis.udel.edu/~carlucci/papers/wghpre.pdf","raw_type":"text"},{"id":"pmh:oai:iris.uniroma1.it:11573/138553","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?eid=2-s2.0-22144483048&partnerID=65&md5=0c168d4e6885e88eda5146b8b34ddd0d","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1705242300","https://openalex.org/W1994332324","https://openalex.org/W2040462567","https://openalex.org/W2065285281","https://openalex.org/W2081739832","https://openalex.org/W2082844458","https://openalex.org/W2154759565","https://openalex.org/W2158569391","https://openalex.org/W2560908651","https://openalex.org/W2743117888","https://openalex.org/W6685292077","https://openalex.org/W6856006254"],"related_works":["https://openalex.org/W3102632868","https://openalex.org/W1998707102","https://openalex.org/W2032649343","https://openalex.org/W1558704946","https://openalex.org/W2905558881","https://openalex.org/W2144739916","https://openalex.org/W4210585271","https://openalex.org/W2017514363","https://openalex.org/W2808746250","https://openalex.org/W2397802583"],"abstract_inverted_index":{"We":[0,36],"define":[1],"a":[2,26,43,51],"direct":[3],"translation":[4],"from":[5],"finite":[6,10,58],"rooted":[7],"trees":[8],"to":[9,25,65,78],"natural":[11,61],"functions":[12],"which":[13],"shows":[14],"that":[15,39],"the":[16,31,40,47,55],"Worm":[17,48],"Principle":[18,49],"introduced":[19],"by":[20],"Lev":[21,79],"Beklemishev":[22,80],"is":[23,81],"equivalent":[24],"very":[27],"slight":[28],"variant":[29],"of":[30,46,57,60,70,74],"well-known":[32],"Kirby-Paris'":[33],"Hydra":[34],"Game.":[35],"further":[37],"show":[38],"elements":[41],"in":[42,54,72],"reduction":[44],"sequence":[45,53],"determine":[50],"bad":[52],"well-quasi-ordering":[56],"sequences":[59],"numbers":[62],"with":[63],"respect":[64],"Friedman's":[66],"gapembeddability.":[67],"A":[68],"characterization":[69],"gap-embeddability":[71],"terms":[73],"provability":[75],"logic":[76],"due":[77],"also":[82],"presented.":[83],"(\u00a9":[84],"2005":[85],"WILEY-VCH":[86],"Verlag":[87],"GmbH":[88],"&":[89],"Co.":[90],"KGaA,":[91],"Weinheim)":[92]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}