Axiomatizácia fyzikálnych systémov a „kvantové logiky‟
Axiomatización de lógicas monádicas con varios cuantificadores cardinales
Axiomatization and undecidability results for linear betweenness relations
Axiomatization of the forcing relation with an application to Peano Arithmetic
Axiomatizing omega and omega-op powers of words
In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.
Axiomatizing omega and omega-op powers of words
In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.
Axiomatizing quantum MV-algebras.
We introduce the notion of p-ideal of a QMV-algebra and we prove that the class of all p-ideals of a QMV-algebra M is in one-to-one correspondence with the class of all congruence relations of M.
Axioms which imply GCH
We propose some new set-theoretic axioms which imply the generalized continuum hypothesis, and we discuss some of their consequences.