We show that the reals in the minimal iterable inner model having n Woodin cardinals are precisely those which are A,‘+ 2 definable from some countable ordinal. (One direction here is due to Hugh Woodin.) It follows that this model satisfies “There is a A.‘+2 well-order of the reals”. We also describe some other connections between the descriptive set theory of projective sets and inner models ...

Let M be a frame matroid or a lifted-graphic matroid and let (G,B) be a biased graph representing M . Given a field F, a canonical F-representation of M particular to (G,B) is a matrix A arising from a gain function over the multiplicative or additive group of F that realizes (G,B). First, for a biased graph (G,B) that is properly unbalanced, loopless, and vertically 2-connected, we show that t...

We study projectively self-dual polygons and curves in the projective plane. Our results provide a partial answer to problem No 1994-17 in the book of Arnold’s problems (2004).

In this article, we show that a linear space whose parameters are those of the complement of a subset in a finite projective plane π of order n such that no line is removed and a sufficient number of lines lost only one point, is projectively extended linear space.