We begin with a ground model satisfying ZF + AD + ACR, and from it construct a generic extension satisfying ZFC + ô2 = w2 + "me nonstationary ideal on w | is w2-saturated". 0. Introduction. The "axiom" of determinacy (henceforth AD) implies many interesting propositions about small cardinal numbers, for example <o, and w2. It is natural to ask whether these propositions are true or, more realis...

Assume ZFC + "There is a weakly compact cardinal" is consistent. Then: (i) For every S c C), ZFC + "S and the monadic theory of o2 are recursive each in the other" is consistent; and (ii) ZFC + "The full second-order theory of w2 is interpretable in the monadic theory of W2" is consistent. Introduction. First we recall the definition of monadic theories. The monadic language corresponding to a ...

The paper is concerned with compact bilinear operators on asymmetric normed spaces. study of multilinear spaces was initiated by Latreche and Dahia (2020) [24]. We go further in this direction prove a Schauder type theorem the compactness adjoint operator ideal properties operators. These extend some results Ramanujan Schock (1985) [34], Ruch (1989) [36], Banach On space forms one introduces an...