S and L fields (Q1089627)

It is known that CH implies the existence of strong S-spaces and strong L-spaces. On the other hand, \(MA+\rceil CH\) implies that there are no such spaces. The author proves that if there exists a strong S-space (strong L-space), then there exists an S-field (L-field, resp.). The main tool of the proof is the author's theorem on embedding of topological spaces into topological fields.