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Hajnal Andréka

Publications and source records attributed to Hajnal Andréka.

10 recordsLinked to original sources
arXiv2026

Permutations, substitutions and finite axiomatizability

Algebras of relations form an algebraic framework for the study of logical systems, extending the correspondence between Boolean algebras and propositional logic. Tarski's representable cylindric algebras $RCA_α$, and Halmos' representable polyadic algebras $RPA_α$ both provide algebraic counterparts to first-order logic. In this paper, we show that the usual finite set of polyadic axioms axiomatize $RPA_α$ over $RDf_α$, the diagonal-free subreducts of elements in $RCA_α$. In short: $RPA_α = PA_α + RDf_α$.

math.LO↗
arXiv2025

Substitutions of variables are finitely axiomatizable over quantifications and permutations

This paper proves that the equational theory of the class $RA_α^{csp}$ of representable polyadic algebras is finitely axiomatizable over its substitution-free reduct $RA_α^{cp}$, for finite $α$. That is, substitutions of variables in finite variable first-order logic can be described by finitely many axioms over the Boolean operations, existential quantifiers and permutations of variables.

math.LO↗
arXiv2021

Complexity in the interdefinability of timelike, lightlike and spacelike relatedness of Minkowski spacetime

Interdefinability of timelike, lightlike and spacelike relatedness of Minkowski spacetime is investigated in detail in the paper, with the aim of finding the simplest definitions. Based on ideas scattered in the literature, definitions are given between any two of these relations that use only 4 variables. All these definitions work over arbitrary Euclidean fields in place of the field of reals, if the dimension n of spacetime is greater than two. If n=2, the definitions work over arbitrary ordered fields except the ones based on lightlike relatedness (where no definition can work by symmetry). None of these relations can be defined from another one using only 3 variables. Our four-variable definitions use only one universal and one existential quantifiers in a specific order. In some of the cases, we show that the order of these quantifiers can be reversed for the price of using twice as many quantifiers. Except two cases, we provide existential/universal definitions using 5 variables or show that no existential/universal definition exists. There are no existential/universal definitions between any two of these relations using only 4 variables. It remains open whether there is an existential (universal) definition of timelike (lightlike) relatedness from spacelike relatedness if $n>2$. Finally, several other open problems related to the quantifier complexity of the simplest possible definitions are given.

math.LO↗
arXiv2018

The variety of coset relation algebras

A coset relation algebra is one embeddable into some full coset relation algebra, the latter is an algebra constructed from a system of groups, a coordinated system of isomorphisms between quotients of these groups, and a system of cosets that are used to "shift" the operation of relative multiplication. We prove that the class of coset relation algebras is equationally axiomatizable (that is to say, it is a variety), but no finite set of equations suffices to axiomatize the class (that is to say, the class is not finitely axiomatizable).

math.LO↗
arXiv2018

A representation theorem for measurable relation algebras with cyclic groups

A relation algebra is measurable if the identity element is a sum of atoms, and the square x;1;x of each subidentity atom x is a sum of non-zero functional elements. These functional elements form a group Gx. We prove that a measurable relation algebra in which the groups Gx are all finite and cyclic is completely representable. A structural description of these algebras is also given.

math.LO↗
arXiv2011

Closed Timelike Curves in Relativistic Computation

In this paper, we investigate the possibility of using closed timelike curves (CTCs) in relativistic hypercomputation. We introduce a wormhole based hypercomputation scenario which is free from the common worries, such as the blueshift problem. We also discuss the physical reasonability of our scenario, and why we cannot simply ignore the possibility of the existence of spacetimes containing CTCs.

gr-qc↗
arXiv2011

A logic road from special relativity to general relativity

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.

gr-qc↗