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On A Problem Concerning Parameter Free Induction
Author(s) -
Adamowicz Z.,
Dimitracopoulos C.
Publication year - 1991
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.19910372304
Subject(s) - mathematics , citation , humanities , library science , calculus (dental) , computer science , philosophy , medicine , dentistry
8 0. Preliminaries In this note we comment on the relationships among local versions of the parameter free induction, collection and pigeonhole schemas. We start by defining the versions that will interest us. We work in the usual language of arithmetic to which a new constant symbol a has been added. P-denotes a finite set of axioms such that if M C P-, then M is the nonnegative part of a commutative discretely ordered ring. Our base theory will be P-+ IZ,, where IZ, denotes the induction schema restricted to Zo formulas with parameters. We recall that in P-+I& every Z,, formula is equivalent to a formula of the form 3XlVx, ... 8, with n alternating quantifiers and Q E 1,.