# Some decidable theories with finitely many covers which are decidable and algorithmically found

Colloquium Mathematicae (1994)

- Volume: 67, Issue: 1, page 61-67
- ISSN: 0010-1354

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topKalfa, Cornelia. "Some decidable theories with finitely many covers which are decidable and algorithmically found." Colloquium Mathematicae 67.1 (1994): 61-67. <http://eudml.org/doc/210263>.

@article{Kalfa1994,

abstract = {In any recursive algebraic language, I find an interval of the lattice of equational theories, every element of which has finitely many covers. With every finite set of equations of this language, an equational theory of this interval is associated, which is decidable with decidable covers that can be algorithmically found. If the language is finite, both this theory and its covers are finitely based. Also, for every finite language and for every natural number n, I construct a finitely based decidable theory together with its exactly n covers which are decidable and finitely based. The construction is algorithmic.},

author = {Kalfa, Cornelia},

journal = {Colloquium Mathematicae},

keywords = {algebraic language; finite basis; decidability; recursive first-order language; lattice of equational theories; covers},

language = {eng},

number = {1},

pages = {61-67},

title = {Some decidable theories with finitely many covers which are decidable and algorithmically found},

url = {http://eudml.org/doc/210263},

volume = {67},

year = {1994},

}

TY - JOUR

AU - Kalfa, Cornelia

TI - Some decidable theories with finitely many covers which are decidable and algorithmically found

JO - Colloquium Mathematicae

PY - 1994

VL - 67

IS - 1

SP - 61

EP - 67

AB - In any recursive algebraic language, I find an interval of the lattice of equational theories, every element of which has finitely many covers. With every finite set of equations of this language, an equational theory of this interval is associated, which is decidable with decidable covers that can be algorithmically found. If the language is finite, both this theory and its covers are finitely based. Also, for every finite language and for every natural number n, I construct a finitely based decidable theory together with its exactly n covers which are decidable and finitely based. The construction is algorithmic.

LA - eng

KW - algebraic language; finite basis; decidability; recursive first-order language; lattice of equational theories; covers

UR - http://eudml.org/doc/210263

ER -

## References

top- [1] A. Ehrenfeucht, Decidability at the theory of one function, Notices Amer. Math. Soc. 6 (1959), 268.
- [2] J. Ježek, Primitive classes of algebras with unary and nullary operations, Colloq. Math. 20 (1969), 159-179. Zbl0188.04801
- [3] C. Kalfa, Covering relation in the language of mono-unary algebras with at most one constant symbol, Algebra Universalis 26 (1989), 143-148. Zbl0675.08002
- [4] G. F. McNulty, Covering in the lattice of equational theories and some properties of term finite theories, ibid. 15 (1982), 115-125. Zbl0509.08013

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