{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T07:54:21Z","timestamp":1772438061410,"version":"3.50.1"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2006,6]]},"abstract":"<jats:p> A statement of hyperarithmetic analysis is a sentence of second order arithmetic S such that for every Y\u2286\u03c9, the minimum \u03c9-model containing Y of RCA<jats:sub>0<\/jats:sub> + S is HYP(Y), the \u03c9-model consisting of the sets hyperarithmetic in Y. We provide an example of a mathematical theorem which is a statement of hyperarithmetic analysis. This statement, that we call INDEC, is due to Jullien [13]. To the author's knowledge, no other already published, purely mathematical statement has been found with this property until now. We also prove that, over RCA<jats:sub>0<\/jats:sub>, INDEC is implied by [Formula: see text] and implies ACA<jats:sub>0<\/jats:sub>, but of course, neither ACA<jats:sub>0<\/jats:sub>, nor ACA <jats:sub>0<\/jats:sub><jats:sup>+<\/jats:sup> imply it. <\/jats:p><jats:p> We introduce five other statements of hyperarithmetic analysis and study the relations among them. Four of them are related to finitely-terminating games. The fifth one, related to iterations of the Turing jump, is strictly weaker than all the other statements that we study in this paper, as we prove using Steel's method of forcing with tagged trees. <\/jats:p>","DOI":"10.1142\/s0219061306000517","type":"journal-article","created":{"date-parts":[[2006,7,24]],"date-time":"2006-07-24T09:26:26Z","timestamp":1153733186000},"page":"89-120","source":"Crossref","is-referenced-by-count":17,"title":["INDECOMPOSABLE LINEAR ORDERINGS AND HYPERARITHMETIC ANALYSIS"],"prefix":"10.1142","volume":"06","author":[{"given":"ANTONIO","family":"MONTALB\u00c1N","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Chicago, Chicago, IL 60637, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1990-0955487-0"},{"key":"rf2","volume-title":"Computable Structures and the Hyperarithmetical Hierarchy","author":"Ash C. 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