Related papers: Implicative algebras II: completeness w.r.t. Set-b…
We describe totally compatible structures on the Jacobson radical of the incidence algebra of a finite poset over a field. We show that such structures are in general non-proper.
Starting from involutive BE algebras, we redefine the orthomodular algebras, by introducing the notion of implicative-orthomodular algebras. We investigate properties of implicative-orthomodular algebras, and give characterizations of these…
We discuss tableaux for the Implicational Propositional Calculus and show how they may be used to establish its completeness.
In this paper, the author gives two methods to construct complete Lie algebras. Both methods show that the derivation algebras of some Lie algebras are complete.
In order to be able to use methods of Universal Algebra for investigating posets, we assign to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to every sectionally pseudocomplemented poset a certain algebra…
We are interested in the problem of translating between two representations of closure systems, namely implicational bases and meet-irreducible elements. Albeit its importance, the problem is open. Motivated by this problem, we introduce…
We construct free cubic implication algebras with finitely many generators, and determine the size of these algebras.
We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…
All exactly integrable systems connected with the semisimple algebras of the second rank with an arbitrary choice of the grading in them are presented in explicit form. General solution of such systems are expressed in terms of the matrix…
One-parameter criterion for 2-equipped posets with respect to cerepresentations is stated and proved. The list of sincere one-parameter 2-equipped posets is given as well as a complex matrix classification of all their indecomposables…
We show that induction over $\Delta(\mathbb R)$-definable well-founded classes is equivalent to the reflection principle which asserts that any true formula of first order set theory with real parameters holds in some transitive set. The…
We prove the complete intersection theorem and complete nontrivial-intersection theorem for systems of set partitions
In a recent work we have shown how to construct an information algebra of coherent sets of gambles defined on general possibility spaces. Here we analyze the connection of such an algebra with the set algebra of subsets of the possibility…
We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…
In Inverse subsumption for complete explanatory induction Yamamoto et al. investigate which inductive logic programming systems can learn a correct hypothesis $H$ by using the inverse subsumption instead of inverse entailment. We prove that…
We provide a characterization of those relation algebras which are isomorphic to the algebras of compatible relations of some $\Z_2$-set. We further prove that this class is finitely axiomatizable in first-order logic in the language of…
The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded…
We give a short, topological proof that all graphs admit tree-decompositions displaying their topological ends.
In a recent paper, two multi-representations for the measurable sets in a computable measure space have been introduced, which prove to be topologically complete w.r.t. certain topological properties. In this contribution, we show them…
Representable implication algebras are known to be axiomatised by a finite number of equations (making the representation and finite representation problems decidable here). We show that this also holds in the context of unary (and binary)…