In the latest in our series reviewing archived copies of Legal Information Management and The Law Librarian – as the journal was once known – LIM’s co-editors leaf through the issues published in 1985.

Human rights courts may be on the cusp of recognizing linkages between the mental health impacts of climate change and human rights. However, several significant obstacles must be overcome before human rights protections are likely to be extended to cover the mental health impacts of climate change. Thus, the push for recognition of human rights protections for people facing mental health harms imposed by climate change must be pursued along with a multifaceted effort that employs regulatory and advocacy strategies alongside litigation, and more clearly establishes the interconnections between mental health, climate change, and human rights.

Hot tap water is the most common source of scald injuries, representing a quarter of all scald injuries requiring hospitalization in the United States. Children and older adults are at increased risk of scald burns. Evidence suggests that poor knowledge of burn risks and treatment among parents and the public may contribute to the burden of scald injuries in children. Medical and injury surveillance categorizes most scald burns as unintentional injuries. However, scald burns can also lead to investigation by the justice system if the injury is suspected to result from abuse or neglect. The Department of Justice recommends assessing criminal intent in childhood scald burns based on traditional indicators derived from medical research: burn uniformity, areas of sparing, burn locations, family history, and speed of medical care. In this study, we present an overview of the existing literature on intentional scald burns in children caused by hot tap water in order to improve their identification and prevention. This systematic review aims to answer two questions: (1) What are the indicators of intentional scald burns in children according to the literature and (2) Is the body of evidence for common indicators of intentional scald burns subject to bias?

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.