{"id":"https://openalex.org/W2743548286","doi":null,"title":"Interstructure Lattices and Types of Peano Arithmetic","display_name":"Interstructure Lattices and Types of Peano Arithmetic","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2743548286","mag":"2743548286"},"language":"en","primary_location":{"id":"pmh:oai:academicworks.cuny.edu:gc_etds-3231","doi":null,"is_oa":true,"landing_page_url":"https://academicworks.cuny.edu/gc_etds/2196","pdf_url":"https://academicworks.cuny.edu/cgi/viewcontent.cgi?article=3231&context=gc_etds","source":{"id":"https://openalex.org/S4377196304","display_name":"CUNY Academic Works (City University of New York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I174216632","host_organization_name":"City University of New York","host_organization_lineage":["https://openalex.org/I174216632"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Dissertations, Theses, and Capstone Projects","raw_type":"doctoral_dissertation"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://academicworks.cuny.edu/cgi/viewcontent.cgi?article=3231&context=gc_etds","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069869531","display_name":"Athar Abdul\u2010Quader","orcid":"https://orcid.org/0000-0001-8993-0025","observed_orcids":["https://orcid.org/0000-0001-8993-0025"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Athar Abdul\u2010Quader","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-8993-0025","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5069869531"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.00019999999494757503,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/peano-arithmetic","display_name":"Peano arithmetic","score":0.9700000286102295},{"id":"https://openalex.org/keywords/elementary-substructures","display_name":"elementary substructures","score":0.8259999752044678},{"id":"https://openalex.org/keywords/finite-distributive-lattices","display_name":"finite distributive lattices","score":0.9010000228881836},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.9240000247955322}],"concepts":[{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.8948007225990295},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6665571928024292},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.551215648651123},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.20745357871055603}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:academicworks.cuny.edu:gc_etds-3231","doi":null,"is_oa":true,"landing_page_url":"https://academicworks.cuny.edu/gc_etds/2196","pdf_url":"https://academicworks.cuny.edu/cgi/viewcontent.cgi?article=3231&context=gc_etds","source":{"id":"https://openalex.org/S4377196304","display_name":"CUNY Academic Works (City University of New York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I174216632","host_organization_name":"City University of New York","host_organization_lineage":["https://openalex.org/I174216632"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Dissertations, Theses, and Capstone Projects","raw_type":"doctoral_dissertation"},{"id":"mag:2743548286","doi":null,"is_oa":false,"landing_page_url":"https://academicworks.cuny.edu/cgi/viewcontent.cgi?article=3231&context=gc_etds","pdf_url":null,"source":{"id":"https://openalex.org/S4306522422","display_name":"PhDT","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"PhDT","raw_type":null}],"best_oa_location":{"id":"pmh:oai:academicworks.cuny.edu:gc_etds-3231","doi":null,"is_oa":true,"landing_page_url":"https://academicworks.cuny.edu/gc_etds/2196","pdf_url":"https://academicworks.cuny.edu/cgi/viewcontent.cgi?article=3231&context=gc_etds","source":{"id":"https://openalex.org/S4377196304","display_name":"CUNY Academic Works (City University of New York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I174216632","host_organization_name":"City University of New York","host_organization_lineage":["https://openalex.org/I174216632"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Dissertations, Theses, and Capstone Projects","raw_type":"doctoral_dissertation"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2743548286.pdf","grobid_xml":"https://content.openalex.org/works/W2743548286.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W83512845","https://openalex.org/W625680999","https://openalex.org/W1975695210","https://openalex.org/W2031450089","https://openalex.org/W2202255769","https://openalex.org/W4205924721"],"related_works":["https://openalex.org/W4406299980","https://openalex.org/W4399554291","https://openalex.org/W1970664602","https://openalex.org/W956611287","https://openalex.org/W2019785716","https://openalex.org/W2042543837","https://openalex.org/W2979943248","https://openalex.org/W4391318768","https://openalex.org/W2054590056","https://openalex.org/W2031450089"],"abstract_inverted_index":{"The":[0],"collection":[1],"of":[2,5,8,21,33,35,52,77,116,125,136,146,170,183,235],"elementary":[3,137,153,176,188,215,245,274,301],"substructures":[4],"a":[6,11,59,123,173,186,202,207,224,243,263,308],"model":[7,50,76,124,169,182,203,265,292],"PA":[9,78,126,171,184],"forms":[10],"lattice,":[12],"and":[13,30,197,206],"is":[14,85,104,122,204,282,307],"referred":[15],"to":[16,45,71,82,102,118,255],"as":[17],"the":[18,22,49,97,144,239,279],"substructure":[19,29],"lattice":[20,281,306],"model.":[23],"In":[24,54,107,139,248],"this":[25,108,128,229,249,253],"thesis,":[26],"we":[27,57,110,142,251],"study":[28,58,143,259],"interstructure":[31,158,280,305],"lattices":[32,44,117],"models":[34,95],"PA.":[36,53],"We":[37,258],"apply":[38],"techniques":[39,112],"used":[40,68],"in":[41,48,65,114,152,163,213,223,242,272,299],"studying":[42],"these":[43],"other":[46,256],"problems":[47],"theory":[51],"Chapter":[55,140],"2,":[56],"problem":[60,161],"that":[61,73,84,91,99,120,167,200,278],"had":[62],"its":[63],"origin":[64],"Simpson,":[66],"who":[67,165],"arithmetic":[69],"forcing":[70],"show":[72,119],"every":[74,100,168,181],"countable":[75,205,264],"has":[79,172,185],"an":[80,132,273,290,300],"expansion":[81,101],"PA\u2217":[83,103],"pointwise":[86,105],"definable.":[87,106],"Enayat":[88],"later":[89],"showed":[90,166,199],"there":[92,121],"are":[93],"2\u21350":[94],"with":[96,127,156],"property":[98,129],"Chapter,":[109,250],"use":[111],"involved":[113],"representations":[115],"which":[130,191,233,267,294],"contains":[131],"infinite":[133],"descending":[134],"chain":[135],"cuts.":[138],"3,":[141],"question":[145],"when":[147],"subsets":[148],"can":[149,210,220,237,269,296],"be":[150,211,221,238,270,297],"coded":[151,212,222,241,271,298],"end":[154,177,189,216,246,275,302],"extensions":[155],"prescribed":[157,284],"lattices.":[159,257],"This":[160],"originated":[162],"Gaifman,":[164],"conservative,":[174],"minimal":[175,187,225,244],"extension.":[178,226,247],"That":[179],"is,":[180],"extension":[190,276,303],"codes":[192],"only":[193],"definable":[194],"sets.":[195],"Kossak":[196],"Paris":[198],"if":[201],"subset":[208],"X":[209],"any":[214],"extension,":[217],"then":[218],"it":[219],"Schmerl":[227],"extended":[228],"work":[230,254],"by":[231],"considering":[232],"collections":[234],"sets":[236,240,268,295],"extend":[252],"two":[260],"questions:":[261],"given":[262,289],"M,":[266,293],"such":[277],"some":[283],"finite":[285,309],"distributive":[286],"lattice;":[287],"and,":[288],"arbitrary":[291],"whose":[304],"Boolean":[310],"algebra?":[311]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2017-08-17T00:00:00"}
