In this paper, we consider determinacy in Brouwerian intuitionistic mathematics. We give some examples of games such that the character of this mathematical setting—the lack of the law of excluded middle and the adoption of continuity principle—makes the behavior of determinacy drastically different from that on the classical setting.

Recent studies have shown that molecular control of inner floral organ identity appears to be largely conserved between monocots and dicots, but little is known regarding the molecular mechanism underlying development of the monocot outer floral organ, a unique floral structure in grasses. In this study, we report the cloning of the rice EXTRA GLUME1 (EG1) gene, a putative lipase gene that spec...

We prove that determinacy for all Boolean combinations of Fσδ (Π 0 3) sets implies the consistency of second-order arithmetic and more. Indeed, it is equivalent to the statement saying that for every set X and every number n, there exists a β-model of Πn-comprehension containing X. We prove this result by providing a careful level-by-level analysis of determinacy at the finite level of the diff...

We prove that the determinacy of Gale-Stewart games whose winning sets are infinitary rational relations accepted by 2-tape Büchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal assumption. Then we prove that winning strategies, when they exist, can be very complex, i.e. highly non-effective, in these games. We prove the...

The following theorems are shown. (A) If ω2 and ω3 have the tree property and either 2א0 = א2 or Ω is measurable thenΠ2 Determinacy holds. (B) If ωn has the tree property for all n < ω, n ≥ 2, and 2<אω = אω then Projective Determinacy holds.

Elizabeth Barnes Forthcoming in Synthese Abstract: In this paper I argue that Gareth Evans’ famous proof of the impossibility of metaphysically indeterminate identity fails on a counterpart-theoretic interpretation of the determinacy operators. I attempt to motivate a counterpart-theoretic reading of the determinacy operators and then show that, understood counterpart-theoretically, Evans’ argu...

We investigate determinacy of delay games with Borel winning conditions, infinite-duration twoplayer games in which one player may delay her moves to obtain a lookahead on her opponent’s moves. First, we prove determinacy of such games with respect to a fixed evolution of the lookahead. However, strategies in such games may depend on information about the evolution. Thus, we introduce different...

In [4], we introduced determinacy schemata motivated by Wadge classes in descriptive set theory. In this paper, we prove that a simple iteration of Σ1 inductive definition implies Sep(∆ 0 2,Σ 0 2) determinacy in the Baire space over RCA0.

We introduce and study the concept of semi determinism A non deterministic generic query is called semi deterministic if any two possible results of the query to a database are isomorphic Semi determinism is a generalization of determinacy proposed by Abiteboul and Kanellakis in the context of object creating query languages The framework of semi deterministic queries is less restrictive than t...

It is known that almost all important set existence axioms in second order arithmetic can be characterized by determinacy schemes of infinite games. In this article, we sketch the proof of the equivalence between Π1 transfinite recursion along ω and determinacy scheme.