On some questions concerning lacunary power series of two variables

On some questions concerning strong compactness

A question of Woodin asks if κ is strongly compact and GCH holds below κ, then must GCH hold everywhere? One variant of this question asks if κ is strongly compact and GCH fails at every regular cardinal δ < κ, then must GCH fail at some regular cardinal δ ≥ κ? Another variant asks if it is possible for GCH to fail at every limit cardinal less than or equal to a strongly compact cardinal κ. We ...

Some Questions concerning Alternative Rings

Some Questions concerning Minimal Structures

An infinite first-order structure is minimal if its each definable subset is either finite or co-finite. We formulate three questions concerning order properties of minimal structures which are motivated by Pillay’s Conjecture (stating that a countable first-order structure must have infinitely many countable, pairwise non-isomorphic elementary extensions). In this article a connection between ...

On Lacunary Trigonometric Series.

1. Fundamental theorem. In a recent paper f I have proved the theorem that if a lacunary trigonometric series CO (1) X(a* cos nk6 + bk sin nk9) (nk+x/nk > q > 1, 0 ^ 0 ^ 2ir) 4-1 has its partial sums uniformly bounded on a set of 0 of positive measure, then the series (2) ¿(a*2 + bk2) k-l converges. The proof was based on the following lemma (which was not stated explicitly but is contained in ...

Some (Wh-) Questions Concerning Passive Interactions

English-speaking children are known to be delayed in their comprehension of passive sentences (Slobin, 1966; Turner & Rommetveit, 1967; Bever, 1970; Maratsos & Ambramovitch, 1975; Maratsos, Fox, Becker, & Chalkley, 1985; Gordon & Chafetz, 1990; Fox & Grodzinsky, 1998; Hirsch & Wexler, 2004a). Additionally, it has been noted that children’s level of passive comprehension is in part determined by...