Notre Dame Journal of Formal Logic 54 (2):137-151 (2013)

Authors
Abstract
For sentences $\phi$ of $L_{\omega_{1},\omega}$, we investigate the question of absoluteness of $\phi$ having models in uncountable cardinalities. We first observe that having a model in $\aleph_{1}$ is an absolute property, but having a model in $\aleph_{2}$ is not as it may depend on the validity of the continuum hypothesis. We then consider the generalized continuum hypothesis context and provide sentences for any $\alpha\in\omega_{1}\setminus\{0,1,\omega\}$ for which the existence of a model in $\aleph_{\alpha}$ is nonabsolute . Finally, we present a complete sentence for which model existence in $\aleph_{3}$ is nonabsolute
Keywords infinitary logic   absoluteness   abstract elementary classes
Categories (categorize this paper)
DOI 10.1215/00294527-1960443
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 65,714
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Squares, Scales and Stationary Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Scales, Squares and Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (1):35-98.
The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.

View all 7 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Splitting Number at Uncountable Cardinals.Jindřich Zapletal - 1997 - Journal of Symbolic Logic 62 (1):35-42.
Consecutive Singular Cardinals and the Continuum Function.Arthur W. Apter & Brent Cody - 2013 - Notre Dame Journal of Formal Logic 54 (2):125-136.
Stationary Subsets of $\lbrack \aleph\omega \rbrack^{<\omegaN}$.Kecheng Liu - 1993 - Journal of Symbolic Logic 58 (4):1201 - 1218.
PFA and Ideals on $\omega_{2}$ Whose Associated Forcings Are Proper.Sean Cox - 2012 - Notre Dame Journal of Formal Logic 53 (3):397-412.
Power-Like Models of Set Theory.Ali Enayat - 2001 - Journal of Symbolic Logic 66 (4):1766-1782.
Limit Ultrapowers and Abstract Logics.Paolo Lipparini - 1987 - Journal of Symbolic Logic 52 (2):437-454.
On Elementary Embeddings From an Inner Model to the Universe.J. Vickers & P. D. Welch - 2001 - Journal of Symbolic Logic 66 (3):1090-1116.
Extender Based Forcings.Moti Gitik & Menachem Magidor - 1994 - Journal of Symbolic Logic 59 (2):445-460.
Proper Forcing and Remarkable Cardinals II.Ralf-Dieter Schindler - 2001 - Journal of Symbolic Logic 66 (3):1481-1492.
A Weak Variation of Shelah's I[Ω₂].William J. Mitchell - 2004 - Journal of Symbolic Logic 69 (1):94-100.

Analytics

Added to PP index
2013-03-01

Total views
16 ( #651,532 of 2,462,595 )

Recent downloads (6 months)
1 ( #449,387 of 2,462,595 )

How can I increase my downloads?

Downloads

My notes