{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T17:48:43Z","timestamp":1776707323832,"version":"3.51.2"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2022,9,6]],"date-time":"2022-09-06T00:00:00Z","timestamp":1662422400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,9,6]],"date-time":"2022-09-06T00:00:00Z","timestamp":1662422400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2023,2]]},"DOI":"10.1007\/s00153-022-00846-2","type":"journal-article","created":{"date-parts":[[2022,9,6]],"date-time":"2022-09-06T18:02:50Z","timestamp":1662487370000},"page":"225-237","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The additive structure of integers with the lower Wythoff sequence"],"prefix":"10.1007","volume":"62","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9090-5898","authenticated-orcid":false,"given":"Mohsen","family":"Khani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Afshin","family":"Zarei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,9,6]]},"reference":[{"key":"846_CR1","doi-asserted-by":"crossref","unstructured":"Du, Ch.F., Mousavi, H., Rowland, E., Schaeffer, L., Shallit, J.: Decision algorithms for Fibonacci-automatic words, III: Enumeration and abelian properties. Internat. J. Found. Comput. Sci. 27(8), 943\u2013963 (2016)","DOI":"10.1142\/S0129054116500386"},{"issue":"6","key":"846_CR2","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1080\/00029890.1960.11989541","volume":"67","author":"DD Wall","year":"1960","unstructured":"Wall, D.D.: Fibonacci Series Modulo $$m$$. Am. Math. Monthly 67(6), 525\u2013532 (1960)","journal-title":"Am. Math. Monthly"},{"key":"846_CR3","first-page":"179","volume":"41","author":"E Zeckendorf","year":"1972","unstructured":"Zeckendorf, E.: Repr\u00e9sentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas. Bull. Soc. Roy. Sci. Li\u00e8ge 41, 179\u2013182 (1972)","journal-title":"Bull. Soc. Roy. Sci. Li\u00e8ge"},{"issue":"1","key":"846_CR4","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1017\/jsl.2017.62","volume":"83","author":"G Conant","year":"2018","unstructured":"Conant, G.: There are no intermediate structures between the group of integers and Presburger arithmetic. J. Symb. Log. 83(1), 187\u2013207 (2018)","journal-title":"J. Symb. Log."},{"key":"846_CR5","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780199219858.001.0001","volume-title":"An Introduction to the Theory of Numbers.","author":"GH Hardy","year":"2008","unstructured":"Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers., 6th edn. Oxford University Press, Oxford (2008)","edition":"6"},{"issue":"1","key":"846_CR6","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1051\/ita\/2016010","volume":"50","author":"H Mousavi","year":"2016","unstructured":"Mousavi, H., Rowland, E., Schaeffer, L., Shallit, J.: Decision algorithms for Fibonacci-automatic words, I: Basic results. RAIRO Theor. Inform. Appl. 50(1), 39\u201366 (2016)","journal-title":"RAIRO Theor. Inform. Appl."},{"key":"846_CR7","doi-asserted-by":"publisher","first-page":"190","DOI":"10.4153\/CMB-1959-025-0","volume":"2","author":"IG Connell","year":"1959","unstructured":"Connell, I.G.: Some properties of Beatty sequences. I. Can. Math. Bull. 2, 190\u2013197 (1959)","journal-title":"Can. Math. Bull."},{"key":"846_CR8","doi-asserted-by":"publisher","first-page":"17","DOI":"10.4153\/CMB-1960-004-2","volume":"3","author":"IG Connell","year":"1960","unstructured":"Connell, I.G.: Some properties of Beatty sequences. II. Can. Math. Bull. 3, 17\u201322 (1960)","journal-title":"Can. Math. Bull."},{"issue":"3","key":"846_CR9","doi-asserted-by":"publisher","first-page":"1041","DOI":"10.1017\/jsl.2017.16","volume":"82","author":"I Kaplan","year":"2017","unstructured":"Kaplan, I., Shelah, S.: Decidability and classification of the theory of integers with primes. J. Symb. Log. 82(3), 1041\u20131050 (2017)","journal-title":"J. Symb. Log."},{"key":"846_CR10","unstructured":"B\u00fcchi, J.R.: \u201cOn a decision method in restricted second order arithmetic\u201d, Logic Methodology and Philosophy of Science(Proc. 1960 Internat. Cogr.), 1\u201311, Stanford Univ. Press, Stanford, Calif., (1962)"},{"key":"846_CR11","unstructured":"Khani, M., Valizadeh, A.N., Zarei, A.: \u201cThe additive structure of integers with a floor function\u201d, arXiv:2110.01673"},{"issue":"3","key":"846_CR12","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.1017\/jsl.2015.34","volume":"81","author":"P Hieronymi","year":"2016","unstructured":"Hieronymi, P.: Expansions of the ordered additive group of real numbers by two discrete subgroups. J. Symb. Log. 81(3), 1007\u20131027 (2016)","journal-title":"J. Symb. Log."},{"issue":"10","key":"846_CR13","doi-asserted-by":"publisher","first-page":"1162","DOI":"10.1016\/j.apal.2019.05.001","volume":"170","author":"P Hieronymi","year":"2019","unstructured":"Hieronymi, P.: When is scalar multiplication decidable? Ann. Pure Appl. Logic 170(10), 1162\u20131175 (2019)","journal-title":"Ann. Pure Appl. Logic"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-022-00846-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00153-022-00846-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-022-00846-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,26]],"date-time":"2023-11-26T17:05:58Z","timestamp":1701018358000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00153-022-00846-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,6]]},"references-count":13,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["846"],"URL":"https:\/\/doi.org\/10.1007\/s00153-022-00846-2","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,6]]},"assertion":[{"value":"24 April 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 August 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 September 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}