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In fact, we show a stronger result: the infinite Ramsey theorem (for tuples of all lengths) is equivalent to the statement that any array <jats:inline-formula><jats:alternatives><jats:tex-math>$$[\\mathbb N]^{n+1}\\rightarrow \\mathbb N^n\\times X$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msup>\n                      <mml:mrow>\n                        <mml:mo>[<\/mml:mo>\n                        <mml:mi>N<\/mml:mi>\n                        <mml:mo>]<\/mml:mo>\n                      <\/mml:mrow>\n                      <mml:mrow>\n                        <mml:mi>n<\/mml:mi>\n                        <mml:mo>+<\/mml:mo>\n                        <mml:mn>1<\/mml:mn>\n                      <\/mml:mrow>\n                    <\/mml:msup>\n                    <mml:mo>\u2192<\/mml:mo>\n                    <mml:msup>\n                      <mml:mi>N<\/mml:mi>\n                      <mml:mi>n<\/mml:mi>\n                    <\/mml:msup>\n                    <mml:mo>\u00d7<\/mml:mo>\n                    <mml:mi>X<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> for a well order\u00a0<jats:italic>X<\/jats:italic> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$n\\in \\mathbb N$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>\u2208<\/mml:mo>\n                    <mml:mi>N<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is good, over the base theory\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathsf {RCA_0}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>RCA<\/mml:mi>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s11083-024-09658-w","type":"journal-article","created":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T07:02:24Z","timestamp":1705993344000},"page":"753-759","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Higman\u2019s Lemma is Stronger for Better Quasi Orders"],"prefix":"10.1007","volume":"41","author":[{"given":"Anton","family":"Freund","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,1,23]]},"reference":[{"issue":"2","key":"9658_CR1","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1112\/plms\/s3-2.1.326","volume":"3","author":"G Higman","year":"1952","unstructured":"Higman, G.: Ordering by divisibility in abstract algebras. 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Cambridge University Press, (2005)","DOI":"10.1017\/9781316755846.020"},{"key":"9658_CR5","unstructured":"Friedman, H.: Some systems of second order arithmetic and their use. In: James, R.D. (ed.) Proceedings of the International Congress of Mathematicians, Vancouver 1974, vol. 1, pp. 235\u2013242. Canadian Mathematical Congress, (1975)"},{"key":"9658_CR6","doi-asserted-by":"crossref","unstructured":"Simpson, S.: Subsystems of Second Order Arithmetic. Perspectives in Logic. Cambridge University Press, (2009)","DOI":"10.1017\/CBO9780511581007"},{"key":"9658_CR7","doi-asserted-by":"publisher","first-page":"431","DOI":"10.2178\/bsl\/1309952320","volume":"17","author":"A Montalb\u00e1n","year":"2011","unstructured":"Montalb\u00e1n, A.: Open questions in reverse mathematics. Bull. Symb. Log. 17, 431\u2013454 (2011)","journal-title":"Bull. Symb. Log."},{"key":"9658_CR8","unstructured":"Shore, R.: On the strength of Fra\u00efss\u00e9\u2019s conjecture. 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