Some questions concerning Hrushovski's amalgamation constructions

Some Questions concerning Hrushovski’s Amalgamation Constructions

In his book on stable groups [Poi87] Poizat writes (with respect to our 1987 understanding of ω-stable fields): ”Nous n’avons pas fait de progrès décisif depuis le temps oú nous chassions les aurochs avec une hache de pierre; nous avons seulment acquis une meilleure comprehension de l’enjeu du problem”. Sadly, there is no better way to describe the current situation with respect to the problem ...

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 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 (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...