{"id":"https://openalex.org/W1970285069","doi":"https://doi.org/10.1016/0168-0072(96)00014-0","title":"Interpolating d-r.e. and REA degrees between r.e. degrees","display_name":"Interpolating d-r.e. and REA degrees between r.e. degrees","publication_year":1996,"publication_date":"1996-04-01","ids":{"openalex":"https://openalex.org/W1970285069","doi":"https://doi.org/10.1016/0168-0072(96)00014-0","mag":"1970285069"},"language":"en","primary_location":{"id":"doi:10.1016/0168-0072(96)00014-0","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0168-0072(96)00014-0","pdf_url":"https://www.sciencedirect.com/science/article/pii/0168007296000140/pdf","source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.sciencedirect.com/science/article/pii/0168007296000140/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028535504","display_name":"M. M. Arslanov","orcid":"https://orcid.org/0000-0001-7773-8394"},"institutions":[{"id":"https://openalex.org/I21203515","display_name":"Kazan Federal University","ror":"https://ror.org/05256ym39","country_code":"RU","type":"education","lineage":["https://openalex.org/I21203515"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Marat Arslanov","raw_affiliation_strings":["Kazan University, Kazan, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kazan University, Kazan, Russia","institution_ids":["https://openalex.org/I21203515"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032435178","display_name":"Steffen Lempp","orcid":"https://orcid.org/0000-0002-2958-4017"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steffen Lempp","raw_affiliation_strings":["University of Wisconsin, Madison, WI 53706-1388, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin, Madison, WI 53706-1388, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041739806","display_name":"Richard A. Shore","orcid":"https://orcid.org/0000-0003-0381-5259"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Richard A. Shore","raw_affiliation_strings":["Cornell University, Ithaca, NY 14853, USA","Cornell University Ithaca, NY 14853, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cornell University, Ithaca, NY 14853, USA","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Cornell University Ithaca, NY 14853, USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5041739806"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":{"value":3390,"currency":"USD","value_usd":3390},"fwci":0.9811,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.73108149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"78","issue":"1-3","first_page":"29","last_page":"56"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9991000294685364,"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":0.9991000294685364,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9805999994277954,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9786999821662903,"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/mathematics","display_name":"Mathematics","score":0.5959149599075317},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32376211881637573}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5959149599075317},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32376211881637573}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/0168-0072(96)00014-0","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0168-0072(96)00014-0","pdf_url":"https://www.sciencedirect.com/science/article/pii/0168007296000140/pdf","source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.127.6523","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.127.6523","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cornell.edu/~shore/papers/pdf/int122.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.44.7237","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.7237","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.cornell.edu/~shore/papers/ps/int122.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1016/0168-0072(96)00014-0","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0168-0072(96)00014-0","pdf_url":"https://www.sciencedirect.com/science/article/pii/0168007296000140/pdf","source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1127925059","display_name":"Mathematical Sciences: Recursion Theory","funder_award_id":"9100114","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2167428356","display_name":"Mathematical Sciences: Logic and Computability","funder_award_id":"9204308","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1970285069.pdf","grobid_xml":"https://content.openalex.org/works/W1970285069.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W44111308","https://openalex.org/W174270456","https://openalex.org/W205625059","https://openalex.org/W772570167","https://openalex.org/W1489060978","https://openalex.org/W1505247831","https://openalex.org/W1531307936","https://openalex.org/W1556584770","https://openalex.org/W1813127884","https://openalex.org/W1924816003","https://openalex.org/W1981509588","https://openalex.org/W1981962996","https://openalex.org/W1984887166","https://openalex.org/W2005798738","https://openalex.org/W2007016528","https://openalex.org/W2010338821","https://openalex.org/W2018697991","https://openalex.org/W2037416374","https://openalex.org/W2044240887","https://openalex.org/W2056414301","https://openalex.org/W2060031586","https://openalex.org/W2070390550","https://openalex.org/W2080106898","https://openalex.org/W2083623332","https://openalex.org/W2083713063","https://openalex.org/W2087237939","https://openalex.org/W2305091430","https://openalex.org/W2333253576","https://openalex.org/W4237518902","https://openalex.org/W4298857464","https://openalex.org/W6608396249","https://openalex.org/W6622378375","https://openalex.org/W6629391523","https://openalex.org/W6630202548","https://openalex.org/W6631775107","https://openalex.org/W6633229802","https://openalex.org/W6640071479","https://openalex.org/W6659610371","https://openalex.org/W6671704992","https://openalex.org/W6818121170","https://openalex.org/W6831908070"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"We":[0],"provide":[1],"three":[2],"new":[3],"results":[4],"about":[5],"interpolating":[6],"2-r.e.":[7],"(i.e.":[8],"d-r.e.)":[9],"or":[10],"2-REA":[11],"(recursively":[12],"enumerable":[13],"in":[14,47,80,96,100,163,185],"and":[15,33,76,98,118],"above)":[16],"degrees":[17,58],"between":[18],"given":[19],"r.e.":[20,51,57,79,89],"degrees:":[21],"Proposition":[22],"1.13.":[23],"If":[24],"c":[25,30,48],"<":[26,42,60,72,74],"h":[27,34,43,59,71],"are":[28,171,198,208,215],"r.e.,":[29],"is":[31,35,39,45,63,78,85,102,110,141,154,223,231],"low":[32],"high,":[36],"then":[37],"there":[38,62,214],"an":[40,86],"a":[41,64,68,73,77,111,126,142,147,155,182],"which":[44,220],"REA":[46,95],"but":[49],"not":[50,172],"Theorem":[52,82],"2.1.":[53],"For":[54],"all":[55],"high":[56],"g":[61,75],"properly":[65],"d-r.e.":[66],"degree":[67],"such":[69,91,212],"that":[70,92,158,167,213,232],"h.":[81],"3.1.":[83],"There":[84],"incomplete":[87],"nonrecursive":[88],"A":[90,97],"every":[93],"set":[94],"recursive":[99],"0\u2032":[101],"of":[103,116,129,133,228,243,246],"r.":[104],"e.":[105],"degree.":[106],"The":[107,121,138,195],"first":[108],"proof":[109,131,150,153],"variation":[112],"on":[113],"the":[114,130,164,168,179,186,199,205,209,229,241,247],"construction":[115,180,230],"Soare":[117],"Stob":[119],"(1982).":[120],"second":[122],"combines":[123],"highness":[124],"with":[125,146],"modified":[127],"version":[128],"strategy":[132],"Cooper":[134],"et":[135],"al.":[136],"(1989).":[137],"third":[139],"theorem":[140],"rather":[143],"surprising":[144],"result":[145],"somewhat":[148],"unusual":[149,226],"strategy.":[151],"Its":[152],"0\u2034":[156],"argument":[157],"at":[159,175,219],"times":[160],"moves":[161],"left":[162],"tree":[165],"so":[166],"accessible":[169,202],"nodes":[170,197,207],"linearly":[173],"ordered":[174],"each":[176],"stage.":[177],"Thus":[178],"lacks":[181],"true":[183,196],"path":[184],"usual":[187],"sense.":[188],"Two":[189],"substitute":[190],"notions":[191],"fill":[192],"this":[193],"role:":[194],"leftmost":[200,210],"ones":[201,211],"infinitely":[203,216],"often;":[204],"semitrue":[206],"many":[217],"stages":[218],"some":[221],"extension":[222],"accessible.":[224],"Another":[225],"feature":[227],"it":[233],"involves":[234],"using":[235],"distinct":[236],"priority":[237],"orderings":[238],"to":[239],"control":[240],"interactions":[242],"different":[244],"parts":[245],"construction.":[248]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}