A “figure in the carpet” (as in the Henry James novella) within the choreography and biography of Merce Cunningham can be found in the relationship of his queerness to his choreographic innovations. Cunningham’s philosophies and practices can be seen to reflect multiple responses to homophobia and sexism—defensive maneuvers, circumventions, and interventions.

We give an explicit quadratic Gröbner basis for generalized Chow rings of supersolvable built lattices, with the help of the operadic structure on geometric lattices introduced in a previous article. This shows that the generalized Chow rings associated to minimal building sets of supersolvable lattices are Koszul. As another consequence, we get that the cohomology algebras of the components of the extended modular operad in genus $0$ are Koszul.

In this thesis, we study the complexity of theorems that may be considered partially impredicative from the point of view of reverse mathematics and Weihrauch degrees.

From the perspective of reverse mathematics and ordinal analysis, the axiomatic system $\mathsf {ATR}_0$ is known as the limit of predicativity, and $\Pi ^1_{1}\text {-}\mathsf {CA}_0$ is known as an impredicative system. In this thesis, we study the complexity of some theorems that are stronger than $\mathsf {ATR}_0$ and weaker than $\Pi ^1_{1}\text {-}\mathsf {CA}_0$ from the point of view of reverse mathematics and Weihrauch degrees.

In Chapter 3, we study some problems related to Knaster–Tarski’s theorem. Knaster–Tarski’s theorem states that any monotone operator on $2^{\omega }$ has a least fixed point. Avigad introduced a weaker variant, $\mathsf {FP}$, which asserts the existence of a fixed point instead of the least fixed point, and proved that $\mathsf {FP}$ for arithmetical operators is equivalent to $\mathsf {ATR}_0$ over $\mathsf {RCA}_0$. In this thesis, we show that $\mathsf {FP}$ for $\Sigma ^0_2$-operators is strictly stronger than $\mathsf {ATR}_2$, a Weihrauch degree corresponding to $\mathsf {ATR}_0$, in terms of Weihrauch reduction. In addition, we study the bottom-up proof of Knaster–Tarski’s theorem. It is known that the least fixed point of a monotone operator is given by the $\omega _1$-times iteration of the operator at the empty set. This implies that any monotone operator involves a hierarchy formed by the iterative applications of the operator, starting with the empty set and reaching the least fixed point. We prove that although the existence of a hierarchy is equivalent to $\mathsf {ATR}_0$ over $\mathsf {ACA}_0$, it is stronger than $\mathsf {C}_{\omega ^{\omega }}$ in the terms of Weirhauch reduction.

In Chapter 5, we study the relative leftmost path principle in Weihrauch degrees. This principle was introduced by Towsner to study partial impredicativity in reverse mathematics. He gave a hierarchy between $\mathsf {ATR}_0$ and $\Pi ^1_1\text {-}\mathsf {CA}_0$ by this principle. We show that this principle also makes a hierarchy between $\mathsf {ATR}_2$ and $\mathsf {C}_{\omega ^{\omega }}$ in Weihrauch degrees. We also show that the relative leftmost path principle is, not the same as, but very close to a variant of $\beta $-model reflection.

In Chapter 6, we introduce a hierarchy dividing $\{\sigma \in \Pi ^1_2 : \Pi ^1_1\text {-}\mathsf {CA}_0 \vdash \sigma \}$. Then, we give some characterizations of this hierarchy using some principles equivalent to $\Pi ^1_1\text {-}\mathsf {CA}_0$: leftmost path principle, Ramsey’s theorem for $\Sigma ^0_n$ classes of $[\mathbb {N}]^{\mathbb {N}}$ and the determinacy of Gale–Stewart game for $(\Sigma ^0_1)_n$ classes. As an application, our hierarchy explicitly shows that the number of applications of the hyperjump operator needed to prove $\Sigma ^0_n$ Ramsey’s theorem or $(\Sigma ^0_1)_n$ determinacy increases when the subscript n increases.

Abstract prepared by Yudai Suzuki.

E-mail: yudai.suzuki.research@gmail.com.

William Labov carried out literacy research throughout his career from the 1960s to 2010s. This developed in tandem with his linguistic documentation of African American Vernacular English. Both began in 1965, when Labov received funding for a three-year fieldwork project on Black youths’ language and schooling in Harlem, New York. Literacy was an important political issue in the 1960s, with substantial funding to raise basic education levels, as part of socioeconomic development agendas. In the US, this coincided with civil rights movements, shifting race relations, and a period of social unrest. In this article, Labov’s first phase of literacy research is traced through this historical moment, from the late 1960s to early 1970s. Also charted is the development of one deficit theory Labov contested during this period—cultural deprivation theory. Three parts are described: foundational conferences in 1964, research and reports from 1965–1968, and centers of contestation from 1969–1972. (Sociolinguistics, ethnography, literacy, reading, cultural deprivation theory)*

In the ethics literature, concern about financial compensation has largely focused on the question of how payment could distort research participants’ perception of risk. Such concern about “undue inducement” has particularly occupied institutional review boards (IRBs) and has often led to conservative judgments about how much financial compensation participants can be offered in exchange for their participation in research. Increasingly, bioethics scholars have argued that such approaches to financial compensation in research could exploit participants, on one hand, or create a barrier to their enrollment, on the other. Despite the vast literature on financial compensation for research, there has been substantially less attention to the potential risk that such payment may pose to research participants. The current system of taxing research compensation is one important example of the financial risks to research participants that warrants more analysis and legislative action.

In his widely anthologized article on the therapy-enhancement distinction, Resnik argues that, from a moral point of view, the claim that something is not health related cannot be a dispositive argument against the permissibility of enhancements. He further states how the permissibility of an intervention will depend on considerations like the intention for its use and the likely consequences that will ensue, and whether these violate any moral standards. Within this framework, in this paper I first argue that enhancements may be morally permissible on autonomy grounds (its political conception); and secondly, that this permissibility does not dissolve a moral distinction between therapies and enhancements, with the reason being that there is still a difference between something being generally permissible (i.e., therapies) and something being conditionally permissible (i.e., enhancements). But that is not all that is important for a moral therapy-enhancement distinction. I also argue that the distinction — apart from being about “permissibility” (at the level of regulation of individual use) — is also about regarding justice more broadly (at the level of what is owed to individuals). What captures the moral distinction more fully is that therapies are, generally speaking, not only morally permissible but also owed to persons (due to being enablers of social cooperation and competition), whereas, at this stage, enhancements can only be morally permissible. I demonstrate the appeal of this view by considering its stability and usefulness across specialized bioethical contexts and across various kinds of enhancements and show that its practical value for policy lies in its legitimizing / anticipatory and prioritizing functions.