We locate winning strategies for various Σ3-games in the L-hierarchy in order to prove the following: THEOREM 1. KP +Σ2-Comprehension ` ∃αLα |=“Σ2-KP +Σ3-Determinacy .” Alternatively: Π3-CA0 `“there is a β-model of ∆ 1 3-CA0 + Σ 0 3Determinacy.” The implication is not reversible. (The antecedent here may be replaced with Π3(Π 1 3)-CA0: Π 1 3 instances of Comprehension with only Π3-lightface def...

The theory of infinite games with slightly imperfect information has been focusing on games with finitely and countably many moves. In this paper, we shift the discussion to games with uncountably many possible moves, introducing the axiom of real Blackwell determinacy Bl-ADR (as an analogue of the axiom of real determinacy ADR). We prove that the consistency strength of Bl-ADR is strictly grea...

It is well known that games with the parity winning condition admit positional determinacy : the winner has always a positional (memoryless) strategy. This property continues to hold if edges rather than vertices are labeled. We show that in this latter case the converse is also true. That is, a winning condition over arbitrary set of colors admits positional determinacy in all games if and onl...

In recent work, Schweber [7] introduces a framework for reverse mathematics in a third order setting and investigates several natural principles of transfinite recursion. The main result of that paper is a proof, using the method of forcing, that in the context of two-person perfect information games with moves in R, open determinacy (Σ1 -DET) is not implied by clopen determinacy (∆ R 1 -DET). ...

We show that Martin’s conjecture on Π1-functions uniformly ≤T -order preserving on a cone implies Π1 Turing Determinacy over ZF+DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant Π2n+1functions is equivalent over ZFC to Σ2n+2-Axiom of Determinacy. As a corollary, the consistency of the conjecture for Π1-uniformly degree invariant functions implies ...

SEPALLATA (SEP) MADS-box genes are required for the regulation of floral meristem determinacy and the specification of sepals, petals, stamens, carpels and ovules, specifically in angiosperms. The SEP subfamily is closely related to the AGAMOUS LIKE6 (AGL6) and SQUAMOSA (SQUA) subfamilies. So far, of these three groups only AGL6-like genes have been found in extant gymnosperms. AGL6 genes are m...

In this article, we report that carpel specification in the Oryza sativa (rice) flower is regulated by the floral homeotic gene DROOPING LEAF (DL) that is distinct from the well-known ABC genes. Severe loss-of-function mutations of DL cause complete homeotic transformation of carpels into stamens. Molecular cloning reveals that DL is a member of the YABBY gene family and is closely related to t...

This paper examines the role of the monetary instrument choice for local equilibrium determinacy under sticky prices and different fiscal policy regimes. Corresponding to Benhabib et al.’s (2001) results for interest rate feedback rules, the money growth rate should not rise by more than one for one with inflation when the primary surplus is raised with public debt. Under an exogenous primary s...

We analyze the set-theoretic strength of determinacy for levels of the Borel hierarchy of the form Σ01+α+3, for α < ω1. Well-known results of H. Friedman and D.A. Martin have shown this determinacy to require α+1 iterations of the Power Set Axiom, but we ask what additional ambient set theory is strictly necessary. To this end, we isolate a family of Π1-reflection principles, Π1-RAPα, whose con...