## 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

symmetric laws, considered as postulates used to define the abstract concept of a

poset. Conversely, a

having two commutative, associative, idempotent, and contractive operations.

symmetric laws, considered as postulates used to define the abstract concept of a

poset. Conversely, a

**lattice**can be defined as an algebraic system, or algebra,having two commutative, associative, idempotent, and contractive operations.

Page 272

The most general finite distributive

generalization of Skolem's theorem. Namely, L is assumed to be any finite

distributive

elements of L; ...

The most general finite distributive

**lattice**may be constructed by a simplegeneralization of Skolem's theorem. Namely, L is assumed to be any finite

distributive

**lattice**, and A is assumed to be the set of all properly join-irreducibleelements of L; ...

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