{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T04:37:11Z","timestamp":1771562231541,"version":"3.50.1"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2020,8]]},"abstract":"<jats:p> We have previously established that [Formula: see text]-comprehension is equivalent to the statement that every dilator has a well-founded Bachmann\u2013Howard fixed point, over [Formula: see text]. In this paper, we show that the base theory can be lowered to [Formula: see text]. We also show that the minimal Bachmann\u2013Howard fixed point of a dilator [Formula: see text] can be represented by a notation system [Formula: see text], which is computable relative to [Formula: see text]. The statement that [Formula: see text] is well founded for any dilator [Formula: see text] will still be equivalent to [Formula: see text]-comprehension. Thus, the latter is split into the computable transformation [Formula: see text] and a statement about the preservation of well-foundedness, over a system of computable mathematics. <\/jats:p>","DOI":"10.1142\/s0219061320500063","type":"journal-article","created":{"date-parts":[[2019,8,21]],"date-time":"2019-08-21T03:08:33Z","timestamp":1566356913000},"page":"2050006","source":"Crossref","is-referenced-by-count":16,"title":["Computable aspects of the Bachmann\u2013Howard principle"],"prefix":"10.1142","volume":"20","author":[{"given":"Anton","family":"Freund","sequence":"first","affiliation":[{"name":"Fachbereich Mathematik, Technische Universit\u00e4t Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany"}]}],"member":"219","published-online":{"date-parts":[[2019,10,8]]},"reference":[{"key":"S0219061320500063BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2009.01.001"},{"key":"S0219061320500063BIB007","first-page":"75","volume":"21","author":"Girard J.-Y.","year":"1981","journal-title":"Ann. Pure Appl. Logic"},{"key":"S0219061320500063BIB008","series-title":"Studies in Proof Theory","volume-title":"Proof Theory and Logical Complexity","volume":"1","author":"Girard J.-Y.","year":"1987"},{"key":"S0219061320500063BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)90076-0"},{"key":"S0219061320500063BIB011","series-title":"Studies in Proof Theory","volume-title":"Theories for Admissible Sets. A Unifying Approach to Proof Theory","author":"J\u00e4ger G.","year":"1986"},{"key":"S0219061320500063BIB012","first-page":"143","volume-title":"Proc. Sympos. Pure Mathematics","author":"Jensen R. B.","year":"1971"},{"key":"S0219061320500063BIB013","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1305810765"},{"key":"S0219061320500063BIB015","doi-asserted-by":"publisher","DOI":"10.2178\/bsl\/1309952320"},{"key":"S0219061320500063BIB016","doi-asserted-by":"publisher","DOI":"10.2307\/2275441"},{"key":"S0219061320500063BIB018","unstructured":"M. Rathjen,  \u03c9-Models and Well-Ordering Principles,  Foundational Adventures: Essays in Honor of Harvey M. Friedman, ed.   Neil Tennant  (College Publications, 2014),  pp. 179\u2013212."},{"key":"S0219061320500063BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-10103-3_19"},{"key":"S0219061320500063BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90192-G"},{"key":"S0219061320500063BIB021","doi-asserted-by":"publisher","DOI":"10.1142\/9781848162778_0011"},{"key":"S0219061320500063BIB023","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511581007"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061320500063","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,29]],"date-time":"2020-07-29T11:53:25Z","timestamp":1596023605000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061320500063"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,8]]},"references-count":14,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2020,8]]}},"alternative-id":["10.1142\/S0219061320500063"],"URL":"https:\/\/doi.org\/10.1142\/s0219061320500063","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,8]]}}}