scholarly journals Distributive p-algebras and double p-algebras having n-permutable congruences

1992 ◽  
Vol 35 (2) ◽  
pp. 301-307 ◽  
Author(s):  
R. Beazer
Keyword(s):  
Order Theory ◽  
Distributive Lattices ◽  
Prime Ideals ◽  
First Order ◽  
First Order Theory ◽  
De Morgan Algebras ◽  
Element Chain

Recent research on aspects of distributive lattices, p-algebras, double p-algebras and de-Morgan algebras (see [2] and the references therein) has led to the consideration of the classes (n≧1) of distributive lattices having no n + 1-element chain in their poset of prime ideals. In [1] we were obliged to characterize the members of by a sentence in the first-order theory of distributive lattices. Subsequently (see [2]), it was realised that coincides with the class of distributive lattices having n+1-permutable congruences. This result is hereby employed to describe those distributive p-algebras and double p-algebras having n-permutable congruences. As an application, new characterizations of those distributive p-algebras and double p-algebras having the property that their compact congruences are principal are obtained. In addition, those varieties of distributive p-algebras and double p-algebras having n-permutable congruences are announced.

Decision problem for separated distributive lattices

1983 ◽  
Vol 48 (1) ◽  
pp. 193-196 ◽  
Author(s):  
Yuri Gurevich
Keyword(s):  
Decision Problem ◽  
Order Theory ◽  
Distributive Lattices ◽  
First Order ◽  
First Order Theory ◽  
Recursively Enumerable ◽  
Recursively Enumerable Sets

AbstractIt is well known that for all recursively enumerable sets X1, X2 there are disjoint recursively enumerable sets Y1 ⊆ Y2 such that Y ⊆ X1, Y2 ⊆ X2 and Y1, ⋃ Y2 = X1 ⋃ X2. Alistair Lachlan called distributive lattices satisfying this property separated. He proved that the first-order theory of finite separated distributive lattices is decidable. We prove here that the first-order theory of all separated distributive lattices is undecidable.

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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