A finitely alternative normal tense logic \(T_{n,m}\) is a normal tense logic characterized by frames in which every point has at most n future alternatives and m past alternatives. The structure of the lattice \(\Lambda (T_{1,1})\) is described. There are \(\aleph _0\) logics in \(\Lambda (T_{1,1})\) without the finite model property (FMP), and only one pretabular logic in \(\Lambda (T_{1,1})\). There are \(2^{\aleph _0}\) logics in \(\Lambda (T_{1,1})\) which are not finitely axiomatizable. For \(nm\ge 2\), there are \(2^{\aleph _0}\) logics in \(\Lambda (T_{n,m})\) without the FMP, and infinitely many pretabular extensions of \(T_{n,m}\).

有限替代的正态时态逻辑\（T_ {n，m} \）是一个特征为帧的正态时态逻辑，其中每个点最多具有n个将来的替代项和m个过去的替代项。描述了晶格\（\ Lambda（T_ {1,1}）\）的结构。\（\ Lambda（T_ {1,1}）\）中有\（\ aleph _0 \）逻辑没有有限模型属性（FMP），\（\ Lambda（T_ {1,1 }）\）。\（\ Lambda（T_ {1,1}）\）中有\（2 ^ {\ aleph _0} \）个逻辑，这些逻辑不是可无限地公理化的。对于\（nm \ ge 2 \），存在\（2 ^ {\ aleph _0} \）逻辑\（\ Lambda（T_ {n，m}）\）不带FMP，并且无数个表格前扩展名\（T_ {n，m} \）。