We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by realtime 1-counter Büchi automata is equivalent to the determinacy of (effective) analytic GaleStewart games which is known to be a large cardinal assumption. We show also that the determinacy of Wadge games between two players in charge of ω-languages accepted by 1-counter Büchi automata is equivalent to the...

The notion of a scale on a pointset is implicit in the classical proof of the Kondo uniformization theorem for E^ sets and in the uniformization theorem of Martin and Solovay [2] for X3 sets, from the assumption that measurable cardinals exist. It was formally isolated in Moschovakis [3], where it was shown (granting projective determinacy) that all projective sets admit projective scales — and...

Grass plants develop unique floral patterns that determine grain production. However, the molecular mechanism underlying the specification of floral organ identities and meristem determinacy, including the interaction among floral homeotic genes, remains largely unknown in grasses. Here, we report the interactions of rice (Oryza sativa) floral homeotic genes, OsMADS3 (a C-class gene), OsMADS13 ...

Determinacy and photoperiod insensitivity are agronomically important traits, selected during or after domestication in common bean. Determinacy reduces aboveground plant biomass and accelerates and synchronizes flowering. Photoperiod insensitivity allows common bean to be grown at higher latitudes under long days. In this study, we attempted to identify Phaseolus vulgaris homologues of 12 Arab...

This paper fills an important gap in the literature on determinacy and existence of sunspot equilibria in stochastic linear self-referential models. The results in this paper demonstrate that heterogeneity in expectations may alter a model’s regions of determinacy. We show how to associate with a heterogeneous expectations model (HE-model) a rational expectations model (ARE-model), the solution...