Models of expansions of equation image with no end extensions

Mathematical Logic Quarterly 57 (4):341-365 (2011)
  Copy   BIBTEX

Abstract

We deal with models of Peano arithmetic. The methods are from creature forcing. We find an expansion of equation image such that its theory has models with no end extensions. In fact there is a Borel uncountable set of subsets of equation image such that expanding equation image by any uncountably many of them suffice. Also we find arithmetically closed equation image with no ultrafilter on it with suitable definability demand. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Categories

Keywords

Reprint years

DOI

10.1002/malq.200910129

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,440

External links

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

Through your library

My notes

Similar books and articles

Compact and Loeb Hausdorff spaces in equation image and the axiom of choice for families of finite sets.Kyriakos Keremedis - 2012 - Mathematical Logic Quarterly 58 (3):130-138.
Strengths and Weaknesses of LH Arithmetic.Chris Pollett & Randall Pruim - 2002 - Mathematical Logic Quarterly 48 (2):221-243.
A p-adic probability logic.Angelina Ilić-Stepić, Zoran Ognjanović, Nebojša Ikodinović & Aleksandar Perović - 2012 - Mathematical Logic Quarterly 58 (4):263-280.
Infinite games in the Cantor space and subsystems of second order arithmetic.Takako Nemoto, MedYahya Ould MedSalem & Kazuyuki Tanaka - 2007 - Mathematical Logic Quarterly 53 (3):226-236.
On the Additive Group Structure of the Nonstandard Models of the Theory of Integers.Hasan Dalgin, Labib Haddad & Mehmet Terziler - 2002 - Mathematical Logic Quarterly 48 (3):403-412.
A p‐adic probability logic.Angelina Ilić-Stepić, Zoran Ognjanović, Nebojša Ikodinović & Aleksandar Perović - 2012 - Mathematical Logic Quarterly 58 (4-5):263-280.
De Morgan Heyting algebras satisfying the identity xn ≈ x.Valeria Castaño & Marcela Muñoz Santis - 2011 - Mathematical Logic Quarterly 57 (3):236-245.
Thin equivalence relations in scaled pointclasses.Ralf Schindler & Philipp Schlicht - 2011 - Mathematical Logic Quarterly 57 (6):615-620.
Remarks on gaps in Dense (Q) / nwd.Teppo Kankaanpää - 2013 - Mathematical Logic Quarterly 59 (1-2):51-61.
The Bergman‐Shelah preorder on transformation semigroups.Zak Mesyan, James D. Mitchell, Michał Morayne & Yann H. Péresse - 2012 - Mathematical Logic Quarterly 58 (6):424-433.
On a positive set theory with inequality.Giacomo Lenzi - 2011 - Mathematical Logic Quarterly 57 (5):474-480.
Weak forms of the Regularity Principle in the presence of equation image.Charalampos Cornaros - 2013 - Mathematical Logic Quarterly 59 (1-2):84-100.
Kolmogorov complexity and characteristic constants of formal theories of arithmetic.Shingo Ibuka, Makoto Kikuchi & Hirotaka Kikyo - 2011 - Mathematical Logic Quarterly 57 (5):470-473.
Do there exist complete sets for promise classes?Olaf Beyersdorff & Zenon Sadowski - 2011 - Mathematical Logic Quarterly 57 (6):535-550.
There is No Low Maximal D.C.E. Degree.Marat Arslanov, S. Barry Cooper & Angsheng Li - 2000 - Mathematical Logic Quarterly 46 (3):409-416.

Analytics

Added to PP
2013-11-03

Downloads
28 (#558,865)

6 months
1 (#1,506,218)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

End extensions and numbers of countable models.Saharon Shelah - 1978 - Journal of Symbolic Logic 43 (3):550-562.
A model of peano arithmetic with no elementary end extension.George Mills - 1978 - Journal of Symbolic Logic 43 (3):563-567.

Add more references