{"id":"https://openalex.org/W2088257207","doi":"https://doi.org/10.2178/jsl/1278682212","title":"Products of some special compact spaces and restricted forms of AC","display_name":"Products of some special compact spaces and restricted forms of AC","publication_year":2010,"publication_date":"2010-07-09","ids":{"openalex":"https://openalex.org/W2088257207","doi":"https://doi.org/10.2178/jsl/1278682212","mag":"2088257207"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1278682212","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1278682212","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Symbolic Logic","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/A5028285276","display_name":"Kyriakos Keremedis","orcid":"https://orcid.org/0000-0001-8453-3477"},"institutions":[{"id":"https://openalex.org/I98805295","display_name":"University of the Aegean","ror":"https://ror.org/03zsp3p94","country_code":"GR","type":"education","lineage":["https://openalex.org/I98805295"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Kyriakos Keremedis","raw_affiliation_strings":["University of the Aegean, Department of Mathematics, Karlovassi, Samos 83200, Greece. E-mail:","University of The Aegean"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of the Aegean, Department of Mathematics, Karlovassi, Samos 83200, Greece. E-mail:","institution_ids":["https://openalex.org/I98805295"]},{"raw_affiliation_string":"University of The Aegean","institution_ids":["https://openalex.org/I98805295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000502133","display_name":"Eleftherios Tachtsis","orcid":"https://orcid.org/0000-0001-9114-3661"},"institutions":[{"id":"https://openalex.org/I98805295","display_name":"University of the Aegean","ror":"https://ror.org/03zsp3p94","country_code":"GR","type":"education","lineage":["https://openalex.org/I98805295"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Eleftherios Tachtsis","raw_affiliation_strings":["University of the Aegean, Department of Statistics and Actuarial-Financial Mathematics, Karlovassi, Samos 83200, Greece. E-mail:","University of The Aegean"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of the Aegean, Department of Statistics and Actuarial-Financial Mathematics, Karlovassi, Samos 83200, Greece. E-mail:","institution_ids":["https://openalex.org/I98805295"]},{"raw_affiliation_string":"University of The Aegean","institution_ids":["https://openalex.org/I98805295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I98805295"],"apc_list":null,"apc_paid":null,"fwci":0.7355,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6995437,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"75","issue":"3","first_page":"996","last_page":"1006"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998000264167786,"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":0.9998000264167786,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9746000170707703,"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/mathematics","display_name":"Mathematics","score":0.8376504182815552},{"id":"https://openalex.org/keywords/tychonoff-space","display_name":"Tychonoff space","score":0.8333706855773926},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.7973200082778931},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.6059470772743225},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.5681930780410767},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5661169290542603},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5583711862564087},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5345209240913391},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.5215649008750916},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.5164373517036438},{"id":"https://openalex.org/keywords/power-set","display_name":"Power set","score":0.5133311152458191},{"id":"https://openalex.org/keywords/separation-axiom","display_name":"Separation axiom","score":0.4858553111553192},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.46831923723220825},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.44799181818962097},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43032339215278625},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.3973497748374939},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.256767213344574},{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.17187082767486572},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07929617166519165},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07875189185142517}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8376504182815552},{"id":"https://openalex.org/C87142424","wikidata":"https://www.wikidata.org/wiki/Q1191433","display_name":"Tychonoff space","level":3,"score":0.8333706855773926},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.7973200082778931},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.6059470772743225},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.5681930780410767},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5661169290542603},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5583711862564087},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5345209240913391},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.5215649008750916},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.5164373517036438},{"id":"https://openalex.org/C100643331","wikidata":"https://www.wikidata.org/wiki/Q205170","display_name":"Power set","level":3,"score":0.5133311152458191},{"id":"https://openalex.org/C40409056","wikidata":"https://www.wikidata.org/wiki/Q1140985","display_name":"Separation axiom","level":3,"score":0.4858553111553192},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.46831923723220825},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.44799181818962097},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43032339215278625},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.3973497748374939},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.256767213344574},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.17187082767486572},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07929617166519165},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07875189185142517},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1278682212","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1278682212","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1278682212","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1278682212","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W799338602","https://openalex.org/W1541012876","https://openalex.org/W1608084331","https://openalex.org/W1980590548","https://openalex.org/W1990682234","https://openalex.org/W1995975622","https://openalex.org/W1998126380","https://openalex.org/W2020053991","https://openalex.org/W2030402678","https://openalex.org/W2065892031","https://openalex.org/W2323053796","https://openalex.org/W2964093406","https://openalex.org/W4235989149","https://openalex.org/W4255340608"],"related_works":["https://openalex.org/W102647493","https://openalex.org/W3197691547","https://openalex.org/W4244304300","https://openalex.org/W177504871","https://openalex.org/W4235989149","https://openalex.org/W4293874521","https://openalex.org/W2055626560","https://openalex.org/W1979204163","https://openalex.org/W2390945607","https://openalex.org/W2088257207"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"establish":[2],"the":[3,14,31,79,108,117,141,169],"following":[4,32],"results:":[5],"1.":[6],"In":[7],"ZF":[8,98,136,139,189],"(i.e.,":[9,138],"Zermelo-Fraenkel":[10],"set":[11,21,73,99,106,150],"theory":[12],"minus":[13,140],"Axiom":[15,142],"of":[16,40,47,55,61,78,110,120,127,143,158,162,172,180],"Choice":[17],"AC),":[18],"for":[19,24],"every":[20,25,71,75,105,149,152],"I":[22,48,62,84,115,128,163,181],"and":[23],"ordinal":[26],"number":[27],"\u03b1":[28],"\u2265":[29],"\u03c9,":[30],"statements":[33],"are":[34],"equivalent:":[35],"(a)":[36],"The":[37,53,68,102,146],"Tychonoff":[38,80,118,170],"product":[39,81,119,171],"\u2223\u03b1\u2223":[41,56],"many":[42,57,122,175],"non-empty":[43,58,123,159,176],"finite":[44,59,89,124,160,177],"discrete":[45,125,178],"subsets":[46,60,126,161,179],"is":[49,63,91,94,129,132,182,185],"compact":[50,92,130,183],".":[51,66,191],"(b)":[52],"union":[54],"well":[64],"orderable":[65],"2.":[67],"statement:":[69,103,147],"For":[70,104,148],"infinite":[72],"I,":[74,107,151],"closed":[76],"subset":[77],"[0,":[82],"1]":[83],"which":[85],"consists":[86],"offunctions":[87],"with":[88],"support":[90],",":[93,131,184],"not":[95,133,186],"provable":[96,134,187],"in":[97,135,188],"theory.":[100],"3.":[101],"principle":[109],"dependent":[111],"choices":[112],"relativised":[113],"to":[114],"implies":[116,168],"countably":[121],"0":[137,154,174,190],"Regularity).":[144],"4.":[145],"\u2135":[153,173],"-":[155],"sized":[156],"family":[157],"has":[164],"a":[165],"choice":[166],"function":[167]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
