An example of a theory without weakly (∑, ∑) -atomic models

1984 ◽  
Vol 23 (3) ◽  
pp. 233-237
Author(s):  
S. A. Chikhachëv
Keyword(s):  
Atomic Models ◽  
Weakly Atomic

Weakly atomic-compact relational structures

1971 ◽  
Vol 36 (1) ◽  
pp. 129-140 ◽  
Author(s):  
G. Fuhrken ◽  
W. Taylor
Keyword(s):  
Abelian Group ◽  
Model Theory ◽  
Compact Abelian Group ◽  
Finite Subset ◽  
Relational Structure ◽  
Similarity Type ◽  
First Order ◽  
Relational Structures ◽  
Order Language ◽  
Weakly Atomic

A relational structure is called weakly atomic-compact if and only if every set Σ of atomic formulas (taken from the first-order language of the similarity type of augmented by a possibly uncountable set of additional variables as “unknowns”) is satisfiable in whenever every finite subset of Σ is so satisfiable. This notion (as well as some related ones which will be mentioned in §4) was introduced by J. Mycielski as a generalization to model theory of I. Kaplansky's notion of an algebraically compact Abelian group (cf. [5], [7], [1], [8]).

scholarly journals THE NUMBER OF ATOMIC MODELS OF UNCOUNTABLE THEORIES

2018 ◽  
Vol 83 (1) ◽  
pp. 84-102
Author(s):  
DOUGLAS ULRICH
Keyword(s):  
Atomic Model ◽  
Complete Theory ◽  
Atomic Models ◽  
Image Position

AbstractWe show there exists a complete theory in a language of size continuum possessing a unique atomic model which is not constructible. We also show it is consistent with $ZFC + {\aleph _1} < {2^{{\aleph _0}}}$ that there is a complete theory in a language of size ${\aleph _1}$ possessing a unique atomic model which is not constructible. Finally we show it is consistent with $ZFC + {\aleph _1} < {2^{{\aleph _0}}}$ that for every complete theory T in a language of size ${\aleph _1}$, if T has uncountable atomic models but no constructible models, then T has ${2^{{\aleph _1}}}$ atomic models of size ${\aleph _1}$.

Atomic Models

1998 ◽  
pp. 269-285
Author(s):  
Narciso Garcia ◽  
Arthur Damask ◽  
Steven Schwarz
Keyword(s):  
Atomic Models

scholarly journals Fully Automated Correlation-Based Refinement of Atomic Models into High Resolution Cryo-EM Density Maps

2018 ◽  
Vol 114 (3) ◽  
pp. 161a
Author(s):  
Andrea C. Vaiana ◽  
Maxim Igaev ◽  
Carsten Kutzner ◽  
Helmut Grubmueller
Keyword(s):  
High Resolution ◽  
Atomic Models ◽  
Density Maps
Sign in / Sign up

Export Citation Format

Share Document