{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T11:11:35Z","timestamp":1780485095760,"version":"3.54.1"},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T00:00:00Z","timestamp":1771459200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    For every natural number\n                    <jats:italic>n<\/jats:italic>\n                    we introduce a new weak choice principle\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0022481224000744_inline1.png\">\n                          <jats:alt-text content-type=\"machine-generated\">n upper R upper C Subscript f i n<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <jats:tex-math>$\\mathrm {nRC_{fin}}$<\/jats:tex-math>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\" display=\"inline\">\n                          <mml:mstyle mathvariant=\"normal\">\n                            <mml:mrow>\n                              <mml:mi>n<\/mml:mi>\n                              <mml:mi>R<\/mml:mi>\n                              <mml:msub>\n                                <mml:mi>C<\/mml:mi>\n                                <mml:mrow>\n                                  <mml:mi>f<\/mml:mi>\n                                  <mml:mi>i<\/mml:mi>\n                                  <mml:mi>n<\/mml:mi>\n                                <\/mml:mrow>\n                              <\/mml:msub>\n                            <\/mml:mrow>\n                          <\/mml:mstyle>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    :\n                  <\/jats:p>\n                  <jats:p>\n                    <jats:italic>Given any infinite set x<\/jats:italic>\n                    ,\n                    <jats:italic>there is an infinite subset<\/jats:italic>\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0022481224000744_inline2.png\">\n                          <jats:alt-text content-type=\"machine-generated\">y subset of or equal to x<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <jats:tex-math>$y\\subseteq x$<\/jats:tex-math>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\" display=\"inline\">\n                          <mml:mrow>\n                            <mml:mi>y<\/mml:mi>\n                            <mml:mo>\u2286<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    <jats:italic>and a selection function f that chooses an n-element subset from every finite<\/jats:italic>\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0022481224000744_inline3.png\">\n                          <jats:alt-text content-type=\"machine-generated\">z subset of or equal to y<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <jats:tex-math>$z\\subseteq y$<\/jats:tex-math>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\" display=\"inline\">\n                          <mml:mrow>\n                            <mml:mi>z<\/mml:mi>\n                            <mml:mo>\u2286<\/mml:mo>\n                            <mml:mi>y<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    <jats:italic>containing at least n elements.<\/jats:italic>\n                  <\/jats:p>\n                  <jats:p>\n                    By constructing new permutation models built on a set of atoms obtained as Fra\u00efss\u00e9 limits, we will study the relation of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0022481224000744_inline4.png\">\n                          <jats:alt-text content-type=\"machine-generated\">n upper R upper C Subscript f i n<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <jats:tex-math>$\\mathrm {nRC_{fin}}$<\/jats:tex-math>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\" display=\"inline\">\n                          <mml:mstyle mathvariant=\"normal\">\n                            <mml:mrow>\n                              <mml:mi>n<\/mml:mi>\n                              <mml:mi>R<\/mml:mi>\n                              <mml:msub>\n                                <mml:mi>C<\/mml:mi>\n                                <mml:mrow>\n                                  <mml:mi>f<\/mml:mi>\n                                  <mml:mi>i<\/mml:mi>\n                                  <mml:mi>n<\/mml:mi>\n                                <\/mml:mrow>\n                              <\/mml:msub>\n                            <\/mml:mrow>\n                          <\/mml:mstyle>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    to the weak choice principles\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0022481224000744_inline5.png\">\n                          <jats:alt-text content-type=\"machine-generated\">upper R upper C Subscript m<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <jats:tex-math>$\\mathrm {RC_m}$<\/jats:tex-math>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\" display=\"inline\">\n                          <mml:mstyle mathvariant=\"normal\">\n                            <mml:mrow>\n                              <mml:mi>R<\/mml:mi>\n                              <mml:msub>\n                                <mml:mi>C<\/mml:mi>\n                                <mml:mi>m<\/mml:mi>\n                              <\/mml:msub>\n                            <\/mml:mrow>\n                          <\/mml:mstyle>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    (that has already been studied in [3] and [6]):\n                  <\/jats:p>\n                  <jats:p>\n                    <jats:italic>Given any infinite set x<\/jats:italic>\n                    ,\n                    <jats:italic>there is an infinite subset<\/jats:italic>\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0022481224000744_inline6.png\">\n                          <jats:alt-text content-type=\"machine-generated\">y subset of or equal to x<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <jats:tex-math>$y\\subseteq x$<\/jats:tex-math>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\" display=\"inline\">\n                          <mml:mrow>\n                            <mml:mi>y<\/mml:mi>\n                            <mml:mo>\u2286<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    <jats:italic>with a choice function f on the family of all m-element subsets of y<\/jats:italic>\n                    .\n                  <\/jats:p>\n                  <jats:p>\n                    Moreover, we prove a stronger analogue of the results in [6] when we study the relation between\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0022481224000744_inline7.png\">\n                          <jats:alt-text content-type=\"machine-generated\">n upper R upper C Subscript f i n<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <jats:tex-math>$\\mathrm {nRC_{fin}}$<\/jats:tex-math>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\" display=\"inline\">\n                          <mml:mstyle mathvariant=\"normal\">\n                            <mml:mrow>\n                              <mml:mi>n<\/mml:mi>\n                              <mml:mi>R<\/mml:mi>\n                              <mml:msub>\n                                <mml:mi>C<\/mml:mi>\n                                <mml:mrow>\n                                  <mml:mi>f<\/mml:mi>\n                                  <mml:mi>i<\/mml:mi>\n                                  <mml:mi>n<\/mml:mi>\n                                <\/mml:mrow>\n                              <\/mml:msub>\n                            <\/mml:mrow>\n                          <\/mml:mstyle>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0022481224000744_inline8.png\">\n                          <jats:alt-text content-type=\"machine-generated\">k upper C Subscript f i n Superscript minus<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <jats:tex-math>$\\mathrm {kC_{fin}^-}$<\/jats:tex-math>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\" display=\"inline\">\n                          <mml:mstyle mathvariant=\"normal\">\n                            <mml:mrow>\n                              <mml:mi>k<\/mml:mi>\n                              <mml:msubsup>\n                                <mml:mi>C<\/mml:mi>\n                                <mml:mrow>\n                                  <mml:mi>f<\/mml:mi>\n                                  <mml:mi>i<\/mml:mi>\n                                  <mml:mi>n<\/mml:mi>\n                                <\/mml:mrow>\n                                <mml:mo>\u2212<\/mml:mo>\n                              <\/mml:msubsup>\n                            <\/mml:mrow>\n                          <\/mml:mstyle>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    which is defined by\n                  <\/jats:p>\n                  <jats:p>\n                    <jats:italic>Given any infinite family<\/jats:italic>\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0022481224000744_inline9.png\">\n                          <jats:alt-text content-type=\"machine-generated\">script upper F<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <jats:tex-math>$\\mathcal {F}$<\/jats:tex-math>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\" display=\"inline\">\n                          <mml:mi mathvariant=\"script\">F<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    <jats:italic>of finite sets of cardinality greater than k<\/jats:italic>\n                    ,\n                    <jats:italic>there is an infinite subfamily<\/jats:italic>\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0022481224000744_inline10.png\">\n                          <jats:alt-text content-type=\"machine-generated\">script upper A subset of or equal to script upper F<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <jats:tex-math>$\\mathcal {A}\\subseteq \\mathcal {F}$<\/jats:tex-math>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\" display=\"inline\">\n                          <mml:mrow>\n                            <mml:mi mathvariant=\"script\">A<\/mml:mi>\n                            <mml:mo>\u2286<\/mml:mo>\n                            <mml:mi mathvariant=\"script\">F<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    <jats:italic>with a selection function f that chooses a k-element subset from each<\/jats:italic>\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0022481224000744_inline11.png\">\n                          <jats:alt-text content-type=\"machine-generated\">upper A element of script upper A<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <jats:tex-math>$A\\in \\mathcal {A}$<\/jats:tex-math>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\" display=\"inline\">\n                          <mml:mrow>\n                            <mml:mi>A<\/mml:mi>\n                            <mml:mo>\u2208<\/mml:mo>\n                            <mml:mi mathvariant=\"script\">A<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    .\n                  <\/jats:p>","DOI":"10.1017\/jsl.2024.74","type":"journal-article","created":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T11:26:27Z","timestamp":1771500387000},"page":"538-555","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["A NEW WEAK CHOICE PRINCIPLE"],"prefix":"10.1017","volume":"91","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6078-7237","authenticated-orcid":false,"given":"LORENZ","family":"HALBEISEN","sequence":"first","affiliation":[{"name":"ETH Z\u00dcRICH"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"RICCARDO","family":"PLATI","sequence":"additional","affiliation":[{"name":"ETH Z\u00dcRICH"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"SALOME","family":"SCHUMACHER","sequence":"additional","affiliation":[{"name":"ETH Z\u00dcRICH"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,2,19]]},"reference":[{"key":"S0022481224000744_r3","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-019-00705-7"},{"key":"S0022481224000744_r8","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2021.20"},{"key":"S0022481224000744_r5","doi-asserted-by":"publisher","DOI":"10.4064\/fm-50-5-475-483"},{"key":"S0022481224000744_r7","doi-asserted-by":"publisher","DOI":"10.2307\/2272420"},{"key":"S0022481224000744_r4","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/059"},{"key":"S0022481224000744_r6","first-page":"57","volume-title":"Models, Algebras, and Proofs","volume":"203","author":"Montenegro","year":"1999"},{"key":"S0022481224000744_r2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-60231-8"},{"key":"S0022481224000744_r1","volume-title":"Set Theory","author":"De La Cruz","year":"1998"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481224000744","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T10:53:53Z","timestamp":1780484033000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481224000744\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,19]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["S0022481224000744"],"URL":"https:\/\/doi.org\/10.1017\/jsl.2024.74","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,19]]},"assertion":[{"value":"\u00a9 The Author(s), 2026. Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}