论文标题
抽象线性空间的同质性
Homogeneity of abstract linear spaces
论文作者
论文摘要
我们讨论抽象线性空间理论中的同质性和普遍性问题，即具有满足自然公理的点和线的结构，如欧几里得或投射几何形状。我们表明，两个最小的投影平面（包括Fano平面）是均匀的，并且假设有连续性假设，存在着一种普遍的基数投射平面$ \ aleph_1 $，该平面在其可数有限且有限的投射式子领域相对于均匀。我们还表明，通用可计数线性空间的存在等同于旧的猜想，即每个有限的线性空间都嵌入了有限的射击平面。
We discuss homogeneity and universality issues in the theory of abstract linear spaces, namely, structures with points and lines satisfying natural axioms, as in Euclidean or projective geometry. We show that the two smallest projective planes (including the Fano plane) are homogeneous and, assuming the continuum hypothesis, there exists a universal projective plane of cardinality $\aleph_1$ that is homogeneous with respect to its countable and finite projective subplanes. We also show that the existence of a generic countable linear space is equivalent to an old conjecture asserting that every finite linear space embeds into a finite projective plane.
