THE JOINT EMBEDDING PROPERTY IN NORMAL OPEN INDUCTION

Authors
OTERO M
Citation
M. Otero, THE JOINT EMBEDDING PROPERTY IN NORMAL OPEN INDUCTION, Annals of pure and applied Logic, 60(3), 1993, pp. 275-290
Citations number
13
Categorie Soggetti
Mathematics, Pure",Mathematics,Mathematics,Mathematics
Journal title
Annals of pure and applied Logic → ACNP
ISSN journal
01680072
Volume
60
Issue
3
Year of publication
1993
Pages
275 - 290
Database
ISI
SICI code
0168-0072(1993)60:3<275:TJEPIN>2.0.ZU;2-M
Abstract
The models of normal open induction are those discretely ordered rings , integrally closed in their fraction field whose nonnegative part sat isfy Peano's induction axioms for open formulas in the language of ord ered semirings. It is known that neither open induction nor the usuall y studied stronger fragments of arithmetic (where induction for quanti fied formulas is allowed), have the joint embedding property. We prove that normal models of open induction have the joint embedding propert y.