We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width (...) reflection in contrast to the usual height reflection of the Lévy–Montague reflection theorem. They are each equiconsistent with ZFC and indeed \Pi_2-conservative over ZFC, being forceable by class forcing while preserving any desired rank-initial segment of the universe. Furthermore, the inner-model reflection principle is a consequence of the existence of sufficient large cardinals, and lightface formulations of the reflection principles follow from the maximality principle MP and from the inner-model hypothesis IMH. We also consider some questions concerning the expressibility of the principles. (shrink)

If there is no inner model with ω many strong cardinals, then there is a set forcing extension of the universe with a projective well-ordering of the reals.

The global pesticide complex has transformed over the past two decades, but social science research has not kept pace. The rise of an enormous generics sector, shifts in geographies of pesticide production, and dynamics of agrarian change have led to more pesticide use, expanding to farm systems that hitherto used few such inputs. Declining effectiveness due to pesticide resistance and anemic institutional support for non-chemical alternatives also have driven intensification in conventional systems. As an inter-disciplinary network of pesticide scholars, we (...) seek to renew the social science research agenda on pesticides to better understand this suite of contemporary changes. To identify research priorities, challenges, and opportunities, we develop the pesticide complex as a heuristic device to highlight the reciprocal and iterative interactions among agricultural practice, the agrochemical industry, civil society-shaped regulatory actions, and contested knowledge of toxicity. Ultimately, collaborations among social scientists and across the social and biophysical sciences can illuminate recent transformations and their uneven socioecological effects. A reinvigorated critical scholarship that embraces the multifaceted nature of pesticides can identify the social and ecological constraints that drive pesticide use and support alternatives to chemically driven industrial agriculture. (shrink)

If the bounded proper forcing axiom BPFA holds and ω 1 = ${\mathrm{\omega }}_{1}^{\mathrm{L}}$ , then there is a lightface ${\mathrm{\Sigma }}_{3}^{1}$ well-ordering of the reals. The argument combines a well-ordering due to Caicedo-Veličković with an absoluteness result for models of MA in the spirit of "David's trick." We also present a general coding scheme that allows us to show that BPFA is equiconsistent with R being lightface ${\mathrm{\Sigma }}_{4}^{1}$ , for many "consistently locally certified" relations R on $\mathrm{\mathbb{R}}$ . (...) This is accomplished through a use of David's trick and a coding through the ∑ 2 stable ordinals of L. (shrink)

In the absence of Woodin cardinals, fine structural inner models for mild large cardinal hypotheses admit forcing extensions where bounded forcing axioms hold and yet the reals are projectively well-ordered.

This volume contains the proceedings of the Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday, held March 27–29, 2015, at Harvard University. It presents a collection of papers related to the work of Woodin, who has been one of the leading figures in set theory since the early 1980s. The topics cover many of the areas central to Woodin's work, including large cardinals, determinacy, descriptive set theory and the continuum problem, as well as connections between set (...) theory and Banach spaces, recursion theory, and philosophy, each reflecting a period of Woodin's career. Other topics covered are forcing axioms, inner model theory, the partition calculus, and the theory of ultrafilters. This volume should make a suitable introduction to Woodin's work and the concerns which motivate it. The papers should be of interest to graduate students and researchers in both mathematics and philosophy of mathematics, particularly in set theory, foundations and related areas. (shrink)