naa a22 4500 510782973 CHVBK 20180411083253.0 cr unu---uuuuu 180411e20130801xx s 000 0 eng 10.1007/s11856-012-0150-9 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0150-9 On the strength of the finite intersection principle [Elektronische Daten] [Damir Dzhafarov, Carl Mummert] We study the logical content of several maximality principles related to the finite intersection principle (FIP) in set theory. Classically, these are all equivalent to the axiom of choice, but in the context of reverse mathematics their strengths vary: some are equivalent to ACA0 over RCA0, while others are strictly weaker and incomparable with WKL0. We show that there is a computable instance of FIP every solution of which has hyperimmune degree, and that every computable instance has a solution in every nonzero c.e. degree. In particular, FIP implies the omitting partial types principle (OPT) over RCA0. We also show that, modulo Σ 2 0 induction, FIP lies strictly below the atomic model theorem (AMT). Hebrew University Magnes Press, 2013 Dzhafarov Damir Department of Mathematics, University of Notre Dame, 255 Hurley Hall, 46556, Notre Dame, Indiana, USA aut Mummert Carl Department of Mathematics, Marshall University, 1 John Marshall Drive, 25755, Huntington, West Virginia, USA aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 196/1(2013-08-01), 345-361 0021-2172 196:1<345 2013 196 11856 https://doi.org/10.1007/s11856-012-0150-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0150-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dzhafarov Damir Department of Mathematics, University of Notre Dame, 255 Hurley Hall, 46556, Notre Dame, Indiana, USA aut NATIONALLICENCE 700 1- Mummert Carl Department of Mathematics, Marshall University, 1 John Marshall Drive, 25755, Huntington, West Virginia, USA aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 196/1(2013-08-01), 345-361 0021-2172 196:1<345 2013 196 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer