The classification of countable models of set theory

, &
Mathematical Logic Quarterly 66 (2):182-189 (2020)
  Copy   BIBTEX

Abstract

We study the complexity of the classification problem for countable models of set theory (). We prove that the classification of arbitrary countable models of is Borel complete, meaning that it is as complex as it can conceivably be. We then give partial results concerning the classification of countable well‐founded models of.

Categories

Add categories

Keywords

Reprint years

DOI

10.1002/malq.201900008

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,571

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

On the classification of vertex-transitive structures.John Clemens, Samuel Coskey & Stephanie Potter - 2019 - Archive for Mathematical Logic 58 (5-6):565-574.
The complexity of classification problems for models of arithmetic.Samuel Coskey & Roman Kossak - 2010 - Bulletin of Symbolic Logic 16 (3):345-358.
A complicated ω-stable depth 2 theory.Martin Koerwien - 2011 - Journal of Symbolic Logic 76 (1):47 - 65.
On the number of countable models of a countable nsop1 theory without weight ω.Byunghan Kim - 2019 - Journal of Symbolic Logic 84 (3):1168-1175.
Superstable theories with few countable models.Lee Fong Low & Anand Pillay - 1992 - Archive for Mathematical Logic 31 (6):457-465.
A decidable Ehrenfeucht theory with exactly two hyperarithmetic models.Robert C. Reed - 1991 - Annals of Pure and Applied Logic 53 (2):135-168.
Order types of ordinals in models of set theory.John E. Hutchinson - 1976 - Journal of Symbolic Logic 41 (2):489-502.
Every countable model of set theory embeds into its own constructible universe.Joel David Hamkins - 2013 - Journal of Mathematical Logic 13 (2):1350006.
End extensions and numbers of countable models.Saharon Shelah - 1978 - Journal of Symbolic Logic 43 (3):550-562.
Comparing Borel Reducibility and Depth of an ω-Stable Theory.Martin Koerwien - 2009 - Notre Dame Journal of Formal Logic 50 (4):365-380.
Omega‐ and Beta‐Models of Alternative Set Theory.Athanassios Tzouvaras - 1994 - Mathematical Logic Quarterly 40 (4):547-569.
Classification theory and 0#.Sy D. Friedman, Tapani Hyttinen & Mika Rautila - 2003 - Journal of Symbolic Logic 68 (2):580-588.
Theories with constants and three countable models.Predrag Tanović - 2007 - Archive for Mathematical Logic 46 (5-6):517-527.
Automatic models of first order theories.Pavel Semukhin & Frank Stephan - 2013 - Annals of Pure and Applied Logic 164 (9):837-854.
A note on countable complete theories having three isomorphism types of countable models.Robert E. Woodrow - 1976 - Journal of Symbolic Logic 41 (3):672-680.

Analytics

Added to PP
2020-06-30

Downloads
10 (#1,185,833)

6 months
4 (#779,649)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Equivalence of generics.Iian B. Smythe - 2022 - Archive for Mathematical Logic 61 (5):795-812.

Add more citations

References found in this work

Infinite time Turing machines.Joel David Hamkins & Andy Lewis - 2000 - Journal of Symbolic Logic 65 (2):567-604.
Models and types of Peano's arithmetic.Haim Gaifman - 1976 - Annals of Mathematical Logic 9 (3):223-306.
Infinite time Turing machines.Joel David Hamkins & Andy Lewis - 2000 - Journal of Symbolic Logic 65 (2):567-604.
Model Theory: An Introduction.David Marker - 2003 - Bulletin of Symbolic Logic 9 (3):408-409.

View all 8 references / Add more references