Motivated by the Ax–Kochen/Ershov principle, a large number of questions about Henselian valued fields have been shown to reduce analogous value group and residue field. In this article, we investigate burden in three-sorted Denef–Pas language. If T is theory admitting relative quantifier elimination (in any characteristic), show that equal sum burdens its As consequence, NTP2 if only field are...

A henselian valued field K is called a tame field if its algebraic closure K̃ is a tame extension, that is, the ramification field of the normal extension K̃|K is algebraically closed. Every algebraically maximal Kaplansky field is a tame field, but not conversely. We develop the algebraic theory of tame fields and then prove Ax–Kochen– Ershov Principles for tame fields. This leads to model compl...

A directed hypergraph is powerful tool to solve the problems that arises in different fields, including computer networks, social networks and collaboration networks. In this research paper, we apply the concept of single-valued neutrosophic sets to directed hypergraphs. We introduce certain new concepts, including single-valued neutrosophic directed hypergraphs, single-valued neutrosophic line...