http://dswarmsikhttkg7jgsoyfiqpj3ighupfrvuz5ri3lu5q2dlqyrpgk7ad.onion/notes/lsg.html
Consider the infinite set of wffs: \[
\mathsf{\{\neg Rab, \neg R^{1}ab, \neg R^{2}ab, \neg R^{3}ab, \dots, \neg R^{n}ab, \dots, R^{*}ab\}}
\] (X) every finite collection of these wffs has a model (Y) the whole infinite set of sentences doesn’t have a model (recall our Definition : “just when there is a finite chain of R-related steps from a to b.”) (iii) For first-order wffs we can’t have both (X) and (Y), according to the compactness theorem, i.e. if every finite subset of some set of...