We prove that every finite lattice L can be embedded in a three-generatedfinite lattice K. We also prove that every algebraic lattice with accessiblecardinality is a complete sublattice of an appropriate algebraic lattice K suchthat K is completely generated by three elements. Note that ZFC has a model inwhich all cardinal numbers are accessible. Our results strengthen P. Crawleyand R. A. Dean's 1959 results by adding finiteness, algebraicity, andcompleteness.
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机译：我们证明了每个有限晶格L都可以嵌入到一个三生成的有限晶格K中。我们还证明了每个具有可访问基数的代数晶格都是一个合适的代数晶格K的一个完整子晶格，使得K完全由三个元素生成。请注意，ZFC具有一个可访问所有基数的模型。我们的结果通过增加有限性，代数性和完备性来增强P. Crawley和R. A. Dean在1959年的结果。
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