Logical matrices and the amalgamation property

Studia Logica ◽  
1982 ◽  
Vol 41 (4) ◽  
pp. 329-341 ◽  
Author(s):  
Janusz Czelakowski
Keyword(s):  
Amalgamation Property ◽  
Logical Matrices

A Note on Saturated Models for Many-Valued Logics

2015 ◽  
Vol 65 (4) ◽  
Author(s):  
Tommaso Flaminio ◽  
Matteo Bianchi
Keyword(s):  
Representation Theorem ◽  
Amalgamation Property ◽  
Short Paper ◽  
Fuzzy Logics ◽  
Saturated Models ◽  
Joint Embedding ◽  
Joint Embedding Property

AbstractIn this short paper we will discuss on saturated and κ-saturated models of many-valued (t-norm based fuzzy) logics. Using these peculiar structures we show a representation theorem à la Di Nola for several classes of algebras including MV, Gödel, product, BL, NM and WNM-algebras. Then, still using (κ)-saturated algebras, we finally show that some relevant subclasses of algebras related to many-valued logics also enjoy the joint embedding property and the amalgamation property.

Reduced products of logical matrices

Studia Logica ◽  
1980 ◽  
Vol 39 (1) ◽  
pp. 19-43 ◽  
Author(s):  
Janusz Czelakowski
Keyword(s):  
Reduced Products ◽  
Logical Matrices

scholarly journals Some remarks on divisible polyhedral MV-algebras

2020 ◽  
Vol 70 (1) ◽  
pp. 51-60
Author(s):  
Serafina Lapenta
Keyword(s):  
Amalgamation Property ◽  
Finite Products ◽  
Finitely Presented ◽  
Mv Algebras

AbstractBuilding on similar notions for MV-algebras, polyhedral DMV-algebras are defined and investigated. For such algebras dualities with suitable categories of polyhedra are established, and the relation with finitely presented Riesz MV-algebras is investigated. Via hull-functors, finite products are interpreted in terms of hom-functors, and categories of polyhedral MV-algebras, polyhedral DMV-algebras and finitely presented Riesz MV-algebras are linked together. Moreover, the amalgamation property is proved for finitely presented DMV-algebras and Riesz MV-algebras, and for polyhedral DMV-algebras.

scholarly journals RELATIVELY EXCHANGEABLE STRUCTURES

2018 ◽  
Vol 83 (2) ◽  
pp. 416-442 ◽  
Author(s):  
HARRY CRANE ◽  
HENRY TOWSNER
Keyword(s):  
Amalgamation Property ◽  
Reference Structure ◽  
Precise Description ◽  
Type Representation ◽  
Relational Structures ◽  
Random Structures ◽  
Image Position

AbstractWe study random relational structures that are relatively exchangeable—that is, whose distributions are invariant under the automorphisms of a reference structure ${M}$. When ${M}$ is ultrahomogeneous and has trivial definable closure, all random structures relatively exchangeable with respect to $m$ satisfy a general Aldous–Hoover-type representation. If ${M}$ also satisfies the n-disjoint amalgamation property (n-DAP) for all $n \ge 1$, then relatively exchangeable structures have a more precise description whereby each component depends locally on ${M}$.

The amalgamation spectrum

2009 ◽  
Vol 74 (3) ◽  
pp. 914-928 ◽  
Author(s):  
John T. Baldwin ◽  
Alexei Kolesnikov ◽  
Saharon Shelah
Keyword(s):  
Natural Number ◽  
Initial Segment ◽  
Amalgamation Property ◽  
Countable Ordinal

AbstractWe study when classes can have the disjoint amalgamation property for a proper initial segment of cardinals.For every natural number k, there is a class Kk, defined by a sentence in Lω1,ω that has no models of cardinality greater than ℶk + 1, but Kk has the disjoint amalgamation property on models of cardinality less than or equal to ℵk − 3 and has models of cardinality ℵk − 1.More strongly, we can have disjoint amalgamation up to ℵ∝ for ∝ < ω1, but have a bound on size of models.For every countable ordinal ∝, there is a class K∝ defined by a sentence in Lω1,ω that has no models of cardinality greater than ℶω1, but K does have the disjoint amalgamation property on models of cardinality less than or equal to ℵ∝.Finally we show that we can extend the ℵ∝ to ℶ∝ in the second theorem consistently with ZFC and while having ℵi ≪ ℶi for 0 < i < ∝. Similar results hold for arbitrary ordinals ∝ with ∣∝∣ = k and Lk + ω.

scholarly journals The strong amalgamation property

1975 ◽  
Vol 33 (1) ◽  
pp. 13-23 ◽  
Author(s):  
Paul Bacsich
Keyword(s):  
Amalgamation Property
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