Elementary extensions of external classes in a nonstandard universe

Studia Logica 60 (2):253-273 (1998)

In continuation of our study of HST, Hrbaek set theory (a nonstandard set theory which includes, in particular, the ZFC Replacement and Separation schemata in the st--language, and Saturation for well-orderable families of internal sets), we consider the problem of existence of elementary extensions of inner "external" subclasses of the HST universe.We show that, given a standard cardinal , any set R * generates an "internal" class S(R) of all sets standard relatively to elements of R, and an "external" class L[S(R)] of all sets constructible (in a sense close to the Gödel constructibility) from sets in S(R). We prove that under some mild saturation-like requirements for R the class L[S(R)] models a certain -version of HST including the principle of +-saturation; moreover, in this case L[S(R)] is an elementary extension of L[S(R)] in the st--language whenever sets R R satisfy the requirements.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
Categories (categorize this paper)
DOI 10.1023/A:1005064032270
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 46,223
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Realism, Nonstandard Set Theory, and Large Cardinals.Karel Hrbacek - 2001 - Annals of Pure and Applied Logic 109 (1-2):15-48.

Add more citations

Similar books and articles

Power-Like Models of Set Theory.Ali Enayat - 2001 - Journal of Symbolic Logic 66 (4):1766-1782.
Standard Sets in Nonstandard Set Theory.Petr Andreev & Karel Hrbacek - 2004 - Journal of Symbolic Logic 69 (1):165-182.
Set Theoretic Properties of Loeb Measure.Arnold W. Miller - 1990 - Journal of Symbolic Logic 55 (3):1022-1036.
Nonstandard Set Theory.Peter Fletcher - 1989 - Journal of Symbolic Logic 54 (3):1000-1008.


Added to PP index

Total views
35 ( #259,264 of 2,285,770 )

Recent downloads (6 months)
6 ( #197,657 of 2,285,770 )

How can I increase my downloads?


My notes

Sign in to use this feature