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We also show that this result does not hold for the limit ordinal <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201800015-math-0007.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201800015:malq201800015-math-0007\"\/>. Moreover, we prove that there is no countable structure <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201800015-math-0008.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201800015:malq201800015-math-0008\"\/> with the degree spectrum <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201800015-math-0009.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201800015:malq201800015-math-0009\"\/> for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201800015-math-0010.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201800015:malq201800015-math-0010\"\/>.<\/jats:p>","DOI":"10.1002\/malq.201800015","type":"journal-article","created":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T09:37:20Z","timestamp":1556789840000},"page":"37-45","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Jump inversions of algebraic structures and \u03a3\u2010definability"],"prefix":"10.1002","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4519-9696","authenticated-orcid":false,"given":"Marat","family":"Faizrahmanov","sequence":"first","affiliation":[{"name":"N. I. Lobachevsky Institute of Mathematics and Mechanics Kazan (Volga Region) Federal University 35 Ulitsa Kremlevskaya Kazan 4200 Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Asher","family":"Kach","sequence":"additional","affiliation":[{"name":"Google LLC 320 N. Morgan Chicago IL 60607 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Iskander","family":"Kalimullin","sequence":"additional","affiliation":[{"name":"N. I. Lobachevsky Institute of Mathematics and Mechanics Kazan (Volga Region) Federal University 35 Ulitsa Kremlevskaya Kazan 4200 Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonio","family":"Montalb\u00e1n","sequence":"additional","affiliation":[{"name":"Department of Mathematics University of California Berkeley, 970 Evans Hall Berkeley CA 94720 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vadim","family":"Puzarenko","sequence":"additional","affiliation":[{"name":"S. L. Sobolev Institute of Mathematics Novosibirsk State University 4 Acad. 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