Kueker's conjecture for superstable theories

1984 ◽  
Vol 49 (3) ◽  
pp. 930-934 ◽  
Author(s):  
Steven Buechler
Keyword(s):  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Superstable Theories ◽  
Infinite Power

AbstractWe prove that if every uncountable model of a first-order theory T is ω-saturated and T is superstable then T is categorical in some infinite power.

Countable models of trivial theories which admit finite coding

1996 ◽  
Vol 61 (4) ◽  
pp. 1279-1286 ◽  
Author(s):  
James Loveys ◽  
Predrag Tanović
Keyword(s):  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Superstable Theories ◽  
Countable Models

AbstractWe prove:Theorem. A complete first order theory in a countable language which is strictly stable, trivial and which admits finite coding hasnonisomorphic countable models.Combined with the corresponding result or superstable theories from [4] our result confirms the Vaught conjecture for trivial theories which admit finite coding.

scholarly journals A first-order theory of Ulm type

Computability ◽  
2019 ◽  
Vol 8 (3-4) ◽  
pp. 347-358
Author(s):  
Matthew Harrison-Trainor
Keyword(s):  
Order Theory ◽  
First Order ◽  
First Order Theory

scholarly journals Quasi-decidability of a Fragment of the First-Order Theory of Real Numbers

2015 ◽  
Vol 57 (2) ◽  
pp. 157-185 ◽  
Author(s):  
Peter Franek ◽  
Stefan Ratschan ◽  
Piotr Zgliczynski
Keyword(s):  
Order Theory ◽  
Real Numbers ◽  
First Order ◽  
First Order Theory

The spectrum of resplendency

1990 ◽  
Vol 55 (2) ◽  
pp. 626-636
Author(s):  
John T. Baldwin
Keyword(s):  
Homogeneous Model ◽  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Uncountable Cardinal ◽  
Recursive Theory ◽  
Finite Language

AbstractLet T be a complete countable first order theory and λ an uncountable cardinal. Theorem 1. If T is not superstable, T has 2λ resplendent models of power λ. Theorem 2. If T is strictly superstable, then T has at least min(2λ, ℶ2) resplendent models of power λ. Theorem 3. If T is not superstable or is small and strictly superstable, then every resplendent homogeneous model of T is saturated. Theorem 4 (with Knight). For each μ ∈ ω ∪ {ω, 2ω} there is a recursive theory in a finite language which has μ resplendent models of power κ for every infinite κ.

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