We give limits defined in terms of abstract pointclasses of the amount of determinacy available in certain canonical inner models involving strong cardinals. We show for example: Theorem A Det(Π1-IND)⇒there exists an inner model with a strong cardinal. Theorem B Det(AQI)⇒there exist type-1 mice and hence inner models with proper classes of strong cardinals where Π1-IND (AQI) is the pointclass o...

Elements of Kleene algebras can be used, among others, as abstractions of the inputoutput semantics of nondeterministic programs or as models for the association of pointers with their target objects. In the first case, one seeks to distinguish the subclass of elements that correspond to deterministic programs. In the second case one is only interested in functional correspondences, since it do...

It is shown that if every real has a sharp and every subset of ω1 is constructible from a real, then there is an inner model with a Woodin cardinal. The following theorem was produced at the AIM meeting “Descriptive Inner Model Theory,” June 02–06, 2014, in a working group whose participants were the authors listed above. The authors would like to thank AIM for their generous hospitality. Theor...

We prove a game theoretic dichotomy for Gδσ sets of block sequences in vector spaces that extends, on the one hand, the block Ramsey theorem of W. T. Gowers proved for analytic sets of block sequences and, on the other hand, M. Davis’ proof of Σ3 determinacy.

Meristems provide new cells to produce organs throughout the life of a plant, and their continuous activity depends on regulatory genes that balance the proliferation of meristem cells with their recruitment to organogenesis. During flower development, this balance is shifted towards organogenesis, causing the meristem to terminate after producing a genetically determined number of organs. In A...

One crucial measure of a species' invasiveness is the rate at which it spreads into a competitor's environment. A heuristic spread rate formula for a spatially explicit, two-species competition model relies on 'linear determinacy' which equates spread rate in the full nonlinear model with spread rate in the system linearized about the leading edge of the invasion. However, linear determinacy is...

According to the ABC(DE) model for flower development, C-genes are required for stamen and carpel development and floral determinacy, and D-genes were proposed to play a unique role in ovule development. Both C- and D-genes belong to the AGAMOUS (AG) subfamily of MADS box transcription factors. We show that the petunia (Petunia hybrida) C-clade genes PETUNIA MADS BOX GENE3 and FLORAL BINDING PR...