Medvedev晶格俘获IPC的自然因子
Natural Factors of the Medvedev Lattice Capturing IPC
摘要：
Skvortsova表明，有一个因素的梅德韦杰夫格捕捉直觉命题逻辑（IPC）。然而，她的因素是不自然的，因为它是以一种特别的方式构建的。我们提出了一个更自然的例子，这样一个因素。我们还证明，对于梅德韦杰夫格的每个非平凡因子，其理论都包含在扬科夫逻辑、IPC的演绎闭包加上弱排中律中。这回答了Sorbi和Terwijn的一个问题。
英文摘要：
Skvortsova showed that there is a factor of the Medvedev lattice which captures intuitionistic propositional logic (IPC). However, her factor is unnatural in the sense that it is constructed in an ad hoc manner. We present a more natural example of such a factor. We also show that for every non-trivial factor of the Medvedev lattice its theory is contained in Jankov's logic, the deductive closure of IPC plus the weak law of the excluded middle. This answers a question by Sorbi and Terwijn.
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。
