Publisher： Cambridge University Press
E-ISSN： 1943-5886|65|2|519-524
ISSN： 0022-4812
Source： The Journal of Symbolic Logic, Vol.65, Iss.2, 2000-06, pp. : 519-524
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Abstract
In [7] the author discussed the relative force —in the set theory ZF— of some representation theorems for ℓ-groups (lattice-ordered groups). One of the theorems not discussed in that paper is the Hahn representation theorem for abelian ℓ-groups. This result, originally proved by Hahn (see [8]) for totally ordered groups and half a century later by Conrad, Harvey and Holland for the general case (see [4]), states that any abelian ℓ-group can be embedded in a Hahn product of copies of R (the real line with its natural totally-ordered group structure). Both proofs rely heavily on Zorn's Lemma which is equivalent to AC (the axiom of choice).
Related content
On the minimal ramification problem for
Compositio Mathematica, Vol. 146, Iss. 3, 2010-05 ,pp. :
Access to resources
Recommend
The Hahn-Schur Theorem on effect algebras
Bulletin of the Australian Mathematical Society, Vol. 75, Iss. 2, 2007-04 ,pp. :
A Hahn-Banach theorem for complex semifields
Bulletin of the Australian Mathematical Society, Vol. 2, Iss. 1, 1970-02 ,pp. :
Borel complexity and computability of the Hahn-Banach Theorem
Archive for Mathematical Logic, Vol. 46, Iss. 7-8, 2008-05 ,pp. :
A representation theorem revisited
By Johnson D.
algebra universalis, Vol. 56, Iss. 3-4, 2007-06 ,pp. :