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The Recursively Mahlo Property in Second Order Arithmetic
Author(s) -
Rathjen Michael
Publication year - 1996
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19960420106
Subject(s) - mathematics , property (philosophy) , second order arithmetic , order (exchange) , mathematics subject classification , set (abstract data type) , characterization (materials science) , arithmetic , discrete mathematics , algebra over a field , pure mathematics , computer science , peano axioms , philosophy , materials science , epistemology , finance , economics , programming language , nanotechnology
The paper characterizes the second order arithmetic theorems of a set theory that features a recursively Mahlo universe; thereby complementing prior proof‐theoretic investigations on this notion. It is shown that the property of being recursively Mahlo corresponds to a certain kind of β‐model reflection in second order arithmetic. Further, this leads to a characterization of the reals recursively computable in the superjump functional. Mathematics Subject Classification: 03F35, 03F15, 03E70.