Perhaps Unidimensional Is Not Unidimensional

Perhaps Unidimensional Is Not Unidimensional

Miller (1956) identified his famous limit of 7 ± 2 items based in part on absolute identification-the ability to identify stimuli that differ on a single physical dimension, such as lines of different length. An important aspect of this limit is its independence from perceptual effects and its application across all stimulus types. Recent research, however, has identified several exceptions. We...

Unidimensional Scaling

On countable simple unidimensional theories

We prove that any countable simple unidimensional theory T is supersimple, under the additional assumptions that T eliminates hyperimaginaries and that the Dφ-ranks are finite and definable.

Vaught's conjecture for unidimensional theories

In Bue93b] we proved Vaught's conjecture for all superstable theories of nite rank; that is, such a theory has countably many or continuum many countable models. While this proof does settle Vaught's conjecture for unidimensional theories a sharper result can be obtained for these theories and in places the proof can be simpliied. Let T be a properly unidimensional theory with < 2 @ 0 many coun...

Countable imaginary simple unidimensional theories

We prove that a countable simple unidimensional theory that eliminates hyperimaginaries is supersimple. This solves a problem of Shelah in the more general context of simple theories under weak assumptions.