{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T02:53:10Z","timestamp":1777517590521,"version":"3.51.4"},"reference-count":23,"publisher":"SAGE Publications","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["COM"],"published-print":{"date-parts":[[2024,1,31]]},"abstract":"<jats:p>We introduce the notion of the first-order part of a problem in the Weihrauch degrees. Informally, the first-order part of a problem P is the strongest problem with codomaixn \u03c9 that is Weihrauch reducible to P. We show that the first-order part is always well-defined, examine some of the basic properties of this notion, and characterize the first-order parts of several well-known problems from the literature.<\/jats:p>","DOI":"10.3233\/com-230446","type":"journal-article","created":{"date-parts":[[2024,2,2]],"date-time":"2024-02-02T10:43:24Z","timestamp":1706870604000},"page":"1-13","source":"Crossref","is-referenced-by-count":2,"title":["On the first-order parts of problems in the Weihrauch degrees"],"prefix":"10.1177","author":[{"given":"Damir\u00a0D.","family":"Dzhafarov","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Connecticut, Storrs, Connecticut, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reed","family":"Solomon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Connecticut, Storrs, Connecticut, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keita","family":"Yokoyama","sequence":"additional","affiliation":[{"name":"Mathematical Institute, Tohoku University, Sendai, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"issue":"6","key":"10.3233\/COM-230446_ref1","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1016\/j.apal.2011.10.006","article-title":"The Bolzano\u2013Weierstrass theorem is the jump of weak K\u0151nig\u2019s lemma","volume":"163","author":"Brattka","year":"2012","journal-title":"Ann. Pure Appl. Logic"},{"key":"10.3233\/COM-230446_ref2","doi-asserted-by":"crossref","unstructured":"V.\u00a0Brattka, G.\u00a0Gherardi and A.\u00a0Pauly, Weihrauch complexity in computable analysis. in: Handbook of Computability and Complexity in Analysis, Theory Appl. Comput. 2021, 367\u2013417.","DOI":"10.1007\/978-3-030-59234-9_11"},{"issue":"4","key":"10.3233\/COM-230446_ref3","doi-asserted-by":"publisher","first-page":"1376","DOI":"10.1007\/s00224-017-9798-1","article-title":"On the uniform computational content of computability theory","volume":"61","author":"Brattka","year":"2017","journal-title":"Theory Comput. Syst."},{"key":"10.3233\/COM-230446_ref4","unstructured":"V.\u00a0Brattka and A.\u00a0Pauly, On the algebraic structure of Weihrauch degrees, Log. Methods Comput. Sci., to appear."},{"issue":"4","key":"10.3233\/COM-230446_ref5","doi-asserted-by":"publisher","first-page":"1278","DOI":"10.1017\/jsl.2017.43","article-title":"On the uniform computational content of Ramsey\u2019s theorem","volume":"82","author":"Brattka","year":"2017","journal-title":"The Journal of Symbolic Logic"},{"issue":"1","key":"10.3233\/COM-230446_ref6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2307\/2694910","article-title":"On the strength of Ramsey\u2019s theorem for pairs","volume":"66","author":"Cholak","year":"2001","journal-title":"J. Symbolic Logic"},{"issue":"2","key":"10.3233\/COM-230446_ref8","doi-asserted-by":"publisher","first-page":"1321","DOI":"10.1090\/tran\/6465","article-title":"On uniform relationships between combinatorial problems","volume":"368","author":"Dorais","year":"2016","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.3233\/COM-230446_ref9","doi-asserted-by":"crossref","unstructured":"R.G.\u00a0Downey and D.R.\u00a0Hirschfeldt, Algorithmic Randomness and Complexity, Theory and Applications of Computability, Springer, New York, 2010.","DOI":"10.1007\/978-0-387-68441-3"},{"issue":"2","key":"10.3233\/COM-230446_ref10","doi-asserted-by":"publisher","first-page":"85","DOI":"10.3233\/COM-180203","article-title":"Ramsey\u2019s theorem and products in the Weihrauch degrees","volume":"9","author":"Dzhafarov","year":"2020","journal-title":"Computability"},{"issue":"1","key":"10.3233\/COM-230446_ref11","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1007\/s11856-012-0150-9","article-title":"On the strength of the finite intersection principle","volume":"196","author":"Dzhafarov","year":"2013","journal-title":"Israel J. Math."},{"key":"10.3233\/COM-230446_ref12","doi-asserted-by":"crossref","unstructured":"D.D.\u00a0Dzhafarov and C.\u00a0Mummert, Reverse Mathematics: Problems, Reductions, and Proofs, Theory and Applications of Computability, Springer, New York, 2022.","DOI":"10.1007\/978-3-031-11367-3"},{"key":"10.3233\/COM-230446_ref13","unstructured":"M.\u00a0Fiori-Carones, L.A.\u00a0Ko\u0142odziejczyk, T.L.\u00a0Wong and K.\u00a0Yokoyama, An isomorphism theorem for models of Weak K\u00f6nig\u2019s lemma without primitive recursion, J. Europ. Math. Soc. (2021)."},{"key":"10.3233\/COM-230446_ref14","doi-asserted-by":"crossref","unstructured":"G.\u00a0Gherardi and A.\u00a0Marcone, How incomputable is the separable Hahn\u2013Banach theorem? in: Proceedings of the Fifth International Conference on Computability and Complexity in Analysis (CCA 2008), Electron. Notes Theor. Comput. Sci., Vol.\u00a0221, Elsevier Sci. B. V., Amsterdam, 2008, pp.\u00a085\u2013102.","DOI":"10.1016\/j.entcs.2008.12.009"},{"key":"10.3233\/COM-230446_ref15","doi-asserted-by":"crossref","unstructured":"P.\u00a0H\u00e1jek, Interpretability and fragments of arithmetic, in: Arithmetic, Proof Theory, and Computational Complexity, Prague, 1991, Oxford Logic Guides, Vol.\u00a023, Oxford Univ. Press, New York, 1993, pp.\u00a0185\u2013196.","DOI":"10.1093\/oso\/9780198536901.003.0008"},{"key":"10.3233\/COM-230446_ref16","doi-asserted-by":"crossref","unstructured":"D.R.\u00a0Hirschfeldt, Slicing the Truth: On the Computable and Reverse Mathematics of Combinatorial Principles, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, World Scientific Publishing Company Incorporated, 2014.","DOI":"10.1142\/9208"},{"key":"10.3233\/COM-230446_ref17","doi-asserted-by":"crossref","unstructured":"D.R.\u00a0Hirschfeldt and C.G.\u00a0Jockusch Jr., On notions of computability-theoretic reduction between \u03a0 2 1 principles, J. Math. Log. 16(1) (2016), 1650002, 59.","DOI":"10.1142\/S0219061316500021"},{"issue":"11","key":"10.3233\/COM-230446_ref18","doi-asserted-by":"publisher","first-page":"5805","DOI":"10.1090\/S0002-9947-09-04847-8","article-title":"The atomic model theorem and type omitting","volume":"361","author":"Hirschfeldt","year":"2009","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.3233\/COM-230446_ref20","doi-asserted-by":"publisher","first-page":"268","DOI":"10.2307\/2272972","article-title":"Jr. Ramsey\u2019s theorem and recursion theory","volume":"37","author":"Jockusch","year":"1972","journal-title":"J. Symbolic Logic"},{"issue":"2","key":"10.3233\/COM-230446_ref21","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1017\/jsl.2021.15","article-title":"Finding descending sequences through ill-founded linear orders","volume":"86","author":"Le Goh","year":"2021","journal-title":"J. Symb. Log."},{"key":"10.3233\/COM-230446_ref22","doi-asserted-by":"crossref","unstructured":"S.G.\u00a0Simpson, Subsystems of Second Order Arithmetic, 2nd edn, Perspectives in Logic, Cambridge University Press, Cambridge, 2009.","DOI":"10.1017\/CBO9780511581007"},{"issue":"4","key":"10.3233\/COM-230446_ref24","doi-asserted-by":"publisher","first-page":"1610","DOI":"10.1017\/jsl.2018.19","article-title":"The strength of Ramsey\u2019s theorem for pairs and arbitrarily many colors","volume":"83","author":"Slaman","year":"2018","journal-title":"J. Symb. Log."},{"key":"10.3233\/COM-230446_ref25","doi-asserted-by":"crossref","unstructured":"R.I.\u00a0Soare, Turing Computability: Theory and Applications, 1st edn, Springer Publishing Company, Incorporated, 2016.","DOI":"10.1007\/978-3-642-31933-4"},{"key":"10.3233\/COM-230446_ref26","doi-asserted-by":"crossref","unstructured":"G.\u00a0Solda and M.\u00a0Valenti, Algebraic properties of the first-order part of a problem, Ann. Pure Appl. Logic 174(7) (2023), 103270.","DOI":"10.1016\/j.apal.2023.103270"}],"container-title":["Computability"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/COM-230446","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T16:03:02Z","timestamp":1777392182000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/COM-230446"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,31]]},"references-count":23,"URL":"https:\/\/doi.org\/10.3233\/com-230446","relation":{},"ISSN":["2211-3576","2211-3568"],"issn-type":[{"value":"2211-3576","type":"electronic"},{"value":"2211-3568","type":"print"}],"subject":[],"published":{"date-parts":[[2024,1,31]]}}}