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Large rigid sets of algebras with respect to embeddability

In: Mathematica Slovaca, vol. 66, no. 2
Gábor Czédli - Danica Jakubíková-Studenovská

Details:

Year, pages: 2016, 401 - 406
Keywords:
embedding, antichain, inaccessible cardinal, rigid algebra, discrete category of algebras, monounary algebra
About article:
Let $τ$ be a nonempty similarity type of algebras. A set $H$ of $τ$-algebras is called rigid with respect to embeddability, if whenever $A,B\in H$ and $φ:A\to B$ is an embedding, then $A=B$ and $φ$ is the identity map. We prove that if $τ$ is a nonempty similarity type and $\mathfrak m$ is a cardinal such that no inaccessible cardinal is smaller than or equal to $\mathfrak m$, then there exists a set $H$ of $τ$-algebras such that $H$ is rigid with respect to embeddability and $|H|=\mathfrak m$. This result strengthens a result proved by the second author in 1980.
How to cite:
ISO 690:
Czédli, G., Jakubíková-Studenovská, D. 2016. Large rigid sets of algebras with respect to embeddability. In Mathematica Slovaca, vol. 66, no.2, pp. 401-406. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0145

APA:
Czédli, G., Jakubíková-Studenovská, D. (2016). Large rigid sets of algebras with respect to embeddability. Mathematica Slovaca, 66(2), 401-406. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0145
About edition:
Published: 1. 4. 2016