Quasi finitely axiomatizable totally categorical theories
Quasi finitely axiomatizable totally categorical theories
复制标题
准有限公理化全范畴理论
DOI：
10.1016/0168-0072(86)90037-0
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发表时间：
1986
期刊：
影响因子：
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通讯作者：
M. Ziegler
中科院分区：
文献类型：
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作者：
Gisela Ahlbrandt;M. Ziegler
如[2]所示，完全范畴结构（即在所有权力中都是范畴结构）不是有限公理化的。另一方面，最简单的全范畴结构：无限集合，有限域上的无限射影或仿射几何，是拟有限公理化的（即由有限数量的公理和无限模式公理化，我们将使用缩写“qfa”）。由于所有全范畴结构都是由这些简单结构“建立”起来的，因此在[2]中推测所有全范畴结构都是准有限公理化的（从现在开始，这意味着：与qfa结构可互定义）。
As was shown in [2], totally categorical structures (ie which are categorical in all powers) are not finitely axiomatizable. On the other hand, the most simple totally categorical structures: infinite sets, infinite projective or affine geometries over a finite field, are quasi finitely axiomatizable (ie axiomatized by a finite number of axioms and the schema of infinity, we will use the abbreviation ‘qfa’. Since all totally categorical structures are ‘built up’from these simple structures, it was conjectured in [2] that all totally categorical structures are quasi finitely axiomatizable (which from now on means: being interdefinable with a qfa structure).