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

Erhard Aichinger; Bernardo Rossi

doi:10.48550/arXiv.1909.10232

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

Erhard Aichinger, Bernardo Rossi

Institute for Algebra

Research output: Working paper and reports › Preprint

Abstract

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

Original language	English
Number of pages	6
DOIs	https://doi.org/10.48550/arXiv.1909.10232
Publication status	Published - Sept 2019

Publication series

Name	arXiv.org
No.	arXiv:1909.10232
ISSN (Print)	2331-8422

Fields of science

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

JKU Focus areas

Digital Transformation

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10.48550/arXiv.1909.10232

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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M3 - Preprint

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

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

Abstract

Publication series

Fields of science

JKU Focus areas

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Clonoids: a unifying approach to equational logic and clones

Cite this