Models without indiscernibles

Journal of Symbolic Logic 43 (3):572-600 (1978)
  Copy   BIBTEX

Abstract

For T any completion of Peano Arithmetic and for n any positive integer, there is a model of T of size $\beth_n$ with no (n + 1)-length sequence of indiscernibles. Hence the Hanf number for omitting types over T, H(T), is at least $\beth_\omega$ . (Now, using an upper bound previously obtained by Julia Knight H (true arithmetic) is exactly $\beth_\omega$ ). If T ≠ true arithmetic, then $H(T) = \beth_{\omega1}$ . If $\delta \not\rightarrow (\rho)^{ , then any completion of Peano Arithmetic has a model of size δ with no set of indiscernibles of size ρ. There are similar results for theories strongly resembling Peano Arithmetic, e.g., ZF + V = L

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,215

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

The argument from almost indiscernibles.Gonzalo Rodriguez-Pereyra - 2017 - Philosophical Studies 174 (12):3005-3020.
The Parthood of Indiscernibles.Lidia Obojska - 2019 - Axiomathes 29 (5):427-439.
Saturated models and models generated by indiscernibles.B. Mariou - 2001 - Journal of Symbolic Logic 66 (1):325-348.
The Identity of Indiscernibles as a Logical Truth.Gerald Keaney - 2007 - Crossroads 1 (2):28-36 Free Online.
Russell and the Identity of Indiscernibles.Michael C. Bradley - 1986 - History of Philosophy Quarterly 3 (3):325 - 333.

Analytics

Added to PP
2009-01-28

Downloads
39 (#301,263)

6 months
2 (#297,972)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

On $n$ -Dependence.Artem Chernikov, Daniel Palacin & Kota Takeuchi - 2019 - Notre Dame Journal of Formal Logic 60 (2):195-214.
Characterization of NIP theories by ordered graph-indiscernibles.Lynn Scow - 2012 - Annals of Pure and Applied Logic 163 (11):1624-1641.
Reducts of random hypergraphs.Simon Thomas - 1996 - Annals of Pure and Applied Logic 80 (2):165-193.
Karp complexity and classes with the independence property.M. C. Laskowski & S. Shelah - 2003 - Annals of Pure and Applied Logic 120 (1-3):263-283.

View all 11 citations / Add more citations

References found in this work

No references found.

Add more references