非标准超限有向图
Nonstandard Transfinite Digraphs
摘要：
非标准有向图和超限有向图已经在两个先前的技术报告中定义和研究。本文研究了非标准和超限的有向图。这就需要在某些方面结合前两部作品中使用的技术。本文首先构造了所有自然数秩的非标准超限有向图。然后，需要构造一类特殊的具有“箭秩”$\vecω$的非标准超限有向图。一旦这样做，就可以获得第一极限序数秩$ω$。这个过程可以继续到更高的级别。
英文摘要：
Nonstandard digraphs and transfinite digraphs have been defined and examined in two prior technical reports. The present work examines digraphs that are both nonstandard and transfinite. This requires a combination in certain ways of the techniques used in the prior two works. We first construct herein nonstandard transfinite digraphs for all the natural-number ranks. Then, a special kind of nonstandard transfinite digraph having the "arrow rank" $\vecω$ needs to be constructed. Once this is done, the first limit-ordinal rank $ω$ can be attained. This procedure can be continued on to still higher ranks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
