On some ascending chains of brouwerian modal logics

This paper specifies classes of framesmaximally omnitemporally characteristic for Thomas' normal modal logicT ₂ ⁺ and for each logic in the ascending chain of Segerberg logics investigated by Segerberg and Hughes and Cresswell. It is shown that distinct a,scending chains of generalized Segerberg logics can be constructed from eachT _n ⁺ logic (n 2). The set containing allT _n ⁺ and Segerberg logics can be totally- (linearly-) ordered but not well-ordered by the inclusion relation. The order type of this ordered set is ^*( + 1). Throughout the paper my approach is fundamentally semantical.I should like to thank Professor G. E. Hughes for helpful comments on an earlier draft of this paper.