A barrier or bridge? Serious problems revealed in the UK citizenship test

Thom Brooks has examined the UK citizenship test and finds that it is highly irrelevant to living in this society, has many inconsistencies, and suffers from serious gender imbalance. To make matters worse, changes to the test this year have transformed it from being a practical trivia quiz to being purely trivial. Greater care needs to be taken to ensure balance and consistency, and it is worth reconsidering the purpose of the test

Inherence and Denomination in the Trinity

The present paper describes an ”ontological square’ mapping possible ways of combining the domains and converse domains of the relations of inherence and denomination. In the context of expounding and extending medieval appropriations of elements drawn from Aristotle’s Categories for theological purposes, the paper uses this square to examine different ways of defining Substance-terms and Accident-terms by reference to inherence and denomination within the constraints imposed by the doctrine of the Trinity. These different approaches are related to particular texts of thinkers including Bonaventure and Gilbert of Poitiers

A note on normal generation and generation of groups

In this note we study sets of normal generators of finitely presented residually $p$-finite groups. We show that if an infinite, finitely presented, residually $p$-finite group $G$ is normally generated by $g_1,\dots,g_k$ with order $n_1,\dots,n_k \in \{1,2,\dots \} \cup \{\infty \}$, then $$\beta_1^{(2)}(G) \leq k-1-\sum_{i=1}^{k} \frac1{n_i},$$ where $\beta_1^{(2)}(G)$ denotes the first $\ell^2$-Betti number of $G$. We also show that any $k$-generated group with $\beta_1^{(2)}(G) \geq k-1-\varepsilon$ must have girth greater than or equal $1/\varepsilon$.Comment: 10 pages, no figure