## Inherently Nonfinitely Based Lattices (1997)

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Venue: | Ann. Pure Appl. Logic |

Citations: | 1 - 1 self |

### BibTeX

@ARTICLE{Freese97inherentlynonfinitely,

author = {Ralph Freese and George F. McNulty and J. B. Nation},

title = {Inherently Nonfinitely Based Lattices},

journal = {Ann. Pure Appl. Logic},

year = {1997},

volume = {115},

pages = {1--3}

}

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### Abstract

We give a general method for constructing lattices L whose equational theories are inherently nonfinitely based. This means that the equational class (that is, the variety) generated by L is locally finite and that L belongs to no locally finite finitely axiomatizable equational class. We also provide an example of a lattice which fails to be inherently nonfinitely based but whose equational theory is not finitely axiomatizable. Key words: lattice, finite axiomatizability, inherently nonfinitely based 1 Introduction A variety is a class of algebras which can be axiomatized by a set of equations (that is, by a set of universal sentences whose quantifier-free parts are equations between terms). According to a classical result of Garrett Birkho# 1 This research was partially supported by NSF grants no. DMS--9500752 and DMS--9400511. The second author thanks the University of Hawaii for its hospitality. Preprint submitted to Elsevier Preprint 12 November 1997 [5] the varieties are exac...