Inherently nonfinitely based lattices
نویسندگان
چکیده
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.
منابع مشابه
A modular inherently nonfinitely based lattice
Proof. As observed in McNulty [7], a locally finite variety V of finite type is inherently nonfinitely based if and only if for infinitely many natural numbers N , there is a non-locally-finite algebra each of whose N -generated subalgebras belongs to V. We prove the theorem by establishing these facts. We assume the reader is familiar with the basic facts of modular lattices; see [1], [2], [6]...
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ورودعنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 115 شماره
صفحات -
تاریخ انتشار 2002