Rigid ℵ ε -saturated models of superstable theories

Ziv Shami; Saharon Shelah

Fundamenta Mathematicae (1999)

  • Volume: 162, Issue: 1, page 37-46
  • ISSN: 0016-2736

Abstract

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In a countable superstable NDOP theory, the existence of a rigid ﬡ ε -saturated model implies the existence of 2 λ rigid ﬡ ε -saturated models of power λ for every λ > 2 ﬡ 0 .

How to cite

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Shami, Ziv, and Shelah, Saharon. "Rigid $ℵ_ε$ -saturated models of superstable theories." Fundamenta Mathematicae 162.1 (1999): 37-46. <http://eudml.org/doc/212411>.

@article{Shami1999,
abstract = {In a countable superstable NDOP theory, the existence of a rigid $ﬡ_ε$-saturated model implies the existence of $2^λ$ rigid $ﬡ_ε$-saturated models of power λ for every $λ > 2^\{ﬡ_0\}$.},
author = {Shami, Ziv, Shelah, Saharon},
journal = {Fundamenta Mathematicae},
keywords = {dimensionally diverse; multidimensional theory; complete type; tree; saturated models; Ehrenfeucht's conjecture; stability; rigid models; saturation; superstable theories; strongly deep; nonorthogonal automorphism},
language = {eng},
number = {1},
pages = {37-46},
title = {Rigid $ℵ_ε$ -saturated models of superstable theories},
url = {http://eudml.org/doc/212411},
volume = {162},
year = {1999},
}

TY - JOUR
AU - Shami, Ziv
AU - Shelah, Saharon
TI - Rigid $ℵ_ε$ -saturated models of superstable theories
JO - Fundamenta Mathematicae
PY - 1999
VL - 162
IS - 1
SP - 37
EP - 46
AB - In a countable superstable NDOP theory, the existence of a rigid $ﬡ_ε$-saturated model implies the existence of $2^λ$ rigid $ﬡ_ε$-saturated models of power λ for every $λ > 2^{ﬡ_0}$.
LA - eng
KW - dimensionally diverse; multidimensional theory; complete type; tree; saturated models; Ehrenfeucht's conjecture; stability; rigid models; saturation; superstable theories; strongly deep; nonorthogonal automorphism
UR - http://eudml.org/doc/212411
ER -

References

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  1. [B] J. T. Baldwin, Fundamentals of Stability Theory, Springer, 1988. 
  2. [Sh-401] S. Shelah, Characterizing an ﬡ ε -saturated model of superstable NDOP theories by its L ∞ , ﬡ ε (d.q)-theory, preprint, 1992. 
  3. [Sh-C] S. Shelah, Classification Theory and the Number of Non-Isomorphic Models, rev. ed., North-Holland, Amsterdam, 1990. 

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