## The new encyclopaedia Britannica: in 32 vol. Macropaedia, Accounting - Architecture, Volume 13 |

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Page 269

Thus the propositions of any deductive system (e.g.,

) form a poset when partially ordered by the implication relation. Mathematics is

concerned with many other familiar partial orderings, such as the relation x < y of

...

Thus the propositions of any deductive system (e.g.,

**lattice**theory or group theory) form a poset when partially ordered by the implication relation. Mathematics is

concerned with many other familiar partial orderings, such as the relation x < y of

...

Page 270

Conversely, a

two commutative, associative, ... The inclusion relation may be defined in terms of

either

Conversely, a

**lattice**can be defined as an algebraic system, or algebra, havingtwo commutative, associative, ... The inclusion relation may be defined in terms of

either

**lattice**operation, because a < y is equivalent either to a A y = a or to a V y ...Page 272

Finite distributive

constructed by a simple generalization of Skolem's theorem. Namely, L is

assumed to be any finite distributive

properly ...

Finite distributive

**lattices**. The most general finite distributive**lattice**may beconstructed by a simple generalization of Skolem's theorem. Namely, L is

assumed to be any finite distributive

**lattice**, and A is assumed to be the set of allproperly ...

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