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On Nonstructure of Elementary Submodels of an Unsuperstable Homogeneous Structure

✍ Scribed by Tapani Hyttinen

Book ID
102941956
Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
504 KB
Volume
43
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

In the first part of this paper we let M be a stable homogeneous model and we prove a nonstructure theorem for the class of all elementary submodels of M, assuming that M is ‘unsuperstable’ and has Skolem functions. In the second part we assume that M is an unstable homogeneous model of large cardinality and we prove a nonstructure theorem for the class of all elementary submodels of M.

📜 SIMILAR VOLUMES

On the Number of Elementary Submodels of
On the Number of Elementary Submodels of an Unsuperstable Homogeneous Structure
✍ Tapani Hyttinen; Saharon Shelah 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 267 KB

## Abstract We show that if __M__ is a stable unsuperstable homogeneous structure, then for most κ ⩽ |__M__|, the number of elementary submodels of __M__ of power κ is 2^κ^.

Finitely generated submodels of an uncou
Finitely generated submodels of an uncountably categorical homogeneous structure
✍ Tapani Hyttinen 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 320 KB

## Abstract We generalize the result of non‐finite axiomatizability of totally categorical first‐order theories from elementary model theory to homogeneous model theory. In particular, we lift the theory of envelopes to homogeneous model theory and develope theory of imaginaries in the case of __ω_