Authors: Farah, Ilijas 
Magidor, Menachem
Title: Omitting types in logic of metric structures
Journal: Journal of Mathematical Logic
Volume: 18
Issue: 2
Issue Date: 1-Dec-2018
Rank: M21a
ISSN: 0219-0613
DOI: 10.1142/S021906131850006X
Abstract: 
This paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenstein, Henson and Usvyatsov. While a complete type is omissible in some model of a countable complete theory if and only if it is not principal, this is not true for the incomplete types by a result of Ben Yaacov. We prove that there is no simple test for determining whether a type is omissible in a model of a theory T in a countable language. More precisely, we find a theory in a countable language such that the set of types omissible in some of its models is a complete ∑21 set and a complete theory in a countable language such that the set of types omissible in some of its models is a complete π11 set. Two more unexpected examples are given: (i) a complete theory T and a countable set of types such that each of its finite sets is jointly omissible in a model of T, but the whole set is not and (ii) a complete theory and two types that are separately omissible, but not jointly omissible, in its models.
Keywords: complete π sets 1 1 | complete ∑ sets 2 1 | Logic of metric structures | omitting types
Publisher: World Scientific

Show full item record

SCOPUSTM   
Citations

5
checked on Sep 17, 2022

Page view(s)

24
checked on Sep 14, 2022

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.