A clonoid based approach to some finiteness results in universal algebraic geometry

Erhard Aichinger; Bernardo Rossi

doi:10.1007/s00012-019-0638-9

A clonoid based approach to some finiteness results in universal algebraic geometry

Erhard Aichinger, Bernardo Rossi

Institute for Algebra

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that for a finite first order structure A and a set of first order formulas Φ in its language with certain closure properties, the finitary relations on A that are definable via formulas in Φ are uniquely determined by those of arity |A|^2.This yields new proofs for some finiteness results from universal algebraic geometry.

Original language	English
Article number	8
Pages (from-to)	81:8:1-7
Number of pages	7
Journal	Algebra Universalis
Volume	81
DOIs	https://doi.org/10.1007/s00012-019-0638-9
Publication status	Published - 2020

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101013 Mathematical logic
102031 Theoretical computer science

JKU Focus areas

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10.1007/s00012-019-0638-9

Clonoids: a unifying approach to equational logic and clones
Aichinger, E. (PI)
FWF - Austrian Science Fund
01.02.2017 → 31.01.2020
Project: Funded research › FWF - Austrian Science Fund

Cite this

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AB - We prove that for a finite first order structure A and a set of first order formulas Φ in its language with certain closure properties, the finitary relations on A that are definable via formulas in Φ are uniquely determined by those of arity |A|^2.This yields new proofs for some finiteness results from universal algebraic geometry.

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DO - 10.1007/s00012-019-0638-9

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A clonoid based approach to some finiteness results in universal algebraic geometry

Abstract

Fields of science

JKU Focus areas

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Clonoids: a unifying approach to equational logic and clones

Cite this