{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T16:20:49Z","timestamp":1767198049228,"version":"build-2238731810"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8867,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1989,12]]},"abstract":"<jats:p>The motivation for the results presented here comes from the following two known theorems which concern countable, recursively saturated models of Peano arithmetic.<\/jats:p>\n                  <jats:p>\n                    (1)\n                    <jats:italic>\n                      if\n                      <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200041141_inline1.png\"\/>\n                      is a countable, recursively saturated model of PA, then for each infinite cardinal \u03ba there is a resplendent\n                      <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200041141_inline2.png\"\/>\n                      which has cardinality \u03ba\n                    <\/jats:italic>\n                    . (See Theorem 10 of [1].)\n                  <\/jats:p>\n                  <jats:p>\n                    (2)\n                    <jats:italic>\n                      if\n                      <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200041141_inline1.png\"\/>\n                      is a countable, recursively saturated model of PA, then\n                      <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200041141_inline1.png\"\/>\n                      is generated by a set of indiscernibles\n                    <\/jats:italic>\n                    . (See [4].)\n                  <\/jats:p>\n                  <jats:p>It will be shown here that (1) and (2) can be amalgamated into a common generalization.<\/jats:p>\n                  <jats:p>\n                    (3)\n                    <jats:italic>\n                      if\n                      <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200041141_inline1.png\"\/>\n                      is a countable, recursively saturated model of PA, then for each infinite cardinal \u03ba there is a resplendent\n                      <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200041141_inline2.png\"\/>\n                      which has cardinality \u03ba and which is generated by a set of indiscernibles\n                    <\/jats:italic>\n                    .\n                  <\/jats:p>\n                  <jats:p>By way of contrast we will also get recursively saturated models of PA which fail to be resplendent and yet are generated by indiscernibles.<\/jats:p>\n                  <jats:p>\n                    (4)\n                    <jats:italic>\n                      if\n                      <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200041141_inline1.png\"\/>\n                      is a countable, recursively saturated model of PA, then for each uncountable cardinal \u03ba there is a \u03ba-like recursively saturated\n                      <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200041141_inline2.png\"\/>\n                      generated by a set of indiscernibles\n                    <\/jats:italic>\n                    .\n                  <\/jats:p>\n                  <jats:p>\n                    None of (1), (2) or (3) is stated in its most general form. We will make some comments concerning their generalizations. From now on let us fix a finite language\n                    <jats:italic>L<\/jats:italic>\n                    ; all structures considered are infinite\n                    <jats:italic>L<\/jats:italic>\n                    -structures unless otherwise indicated.\n                  <\/jats:p>","DOI":"10.2307\/2274820","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:32:43Z","timestamp":1146940363000},"page":"1382-1388","source":"Crossref","is-referenced-by-count":3,"title":["Large resplendent models generated by indiscernibles"],"prefix":"10.1017","volume":"54","author":[{"given":"James H.","family":"Schmerl","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200041141","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T06:33:50Z","timestamp":1679466830000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200041141\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,12]]},"references-count":0,"aliases":["10.1017\/s0022481200041141"],"journal-issue":{"issue":"4","published-print":{"date-parts":[[1989,12]]}},"alternative-id":["S0022481200041141"],"URL":"https:\/\/doi.org\/10.2307\/2274820","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,12]]}}}