The discussion centers on defining a V-sentence phi that allows for arbitrarily large finite models while ensuring that any finite model G is a connected graph. Participants suggest exploring various classes of connected graphs, such as bipartite graphs, complete graphs, and planar graphs, to identify a simple first-order characterization for phi. The goal is to construct a first-order statement about arbitrary vertices that guarantees a connected graph but does not hold for every connected graph. Additionally, there are reminders about proper forum etiquette, including posting in the homework section and providing clear definitions of terms.
PREREQUISITESThis discussion is beneficial for students and researchers in mathematical logic, particularly those focusing on graph theory and model theory, as well as educators looking to enhance their understanding of V-sentences and graph classifications.
This and the other two problems you posted look like homework. They should be posted in the homework section. When you post there, you should follow the guidelines there, which include showing your own work and not just asking other people to answer your questions. Also, as a general rule no matter where you post on the forum, you should use proper spelling and grammar, and define any special terms (e.g. what's a "V-sentence"?) so that it's easy for others to read.sara15 said:how to define a V-sentence phi such that phi has aebitrarily large finite models and for any finite model G , G is a connected graph. after that to find a connected graph that does not model the sentence phi. please explain it to me.