arXiv subjects
Publications and source records attributed to P. L. Robinson.
We take points and planes as fundamental, lines as derived, in an axiomatic formulation of three-dimensional projective space, the self-dual nature of which formulation renders automatic the principle of duality.
We take a third-order approach to the fourth Painlevé equation and indicate the value of such an approach to other second-order ODEs in the Painlevé-Gambier list of 50.
We examine the relationship between the homogeneous second Painlevé equation and equation ${\bf XX}$ from the master list recorded by Ince.
We consider the (real) fourth Painlevé equation in which both parameters vanish, analyzing the square-roots of its solutions and paying special attention to their zeros.
We offer elementary proofs for fundamental properties of solutions to the homogeneous second Painlevé equation.
We offer elementary proofs for fundamental properties of the unique triple-zero solution to the first Painlevé equation.
We investigate the Hamiltonian system generated by a homogeneous binary polynomial $U$ of order greater than four. In particular, we study the circumstances under which the associated Hessian is a Weierstrass $\wp$ function and find that the vanishing of two covariants of $U$ is involved.
The vanishing of the invariant $g_3$ attached to a lattice $Λ$ singles out a midpoint lattice and yields a square-root of the associated Weierstrass function $\wp_Λ$.
We modify the Whittaker-Watson account of the Eisenstein approach to the trigonometric functions, basing these functions independently on the Eisenstein function $\varepsilon_2$.
For formulas of the Implicational Propositional Calculus (IPC) that are theorems of the classical Propositional Calculus (PC) we show that PC proofs yield IPC proofs. As a consequence, completeness of PC yields completeness of IPC.
We prove a version of the Grätzer-Schmidt theorem for the Lindenbaum-Tarski algebra associated to the Implicational Propositional Calculus.
We study $Q$-tableaux and axiom systems that they engender, producing a new proof that the Implicational Propositional Calculus is complete.
We discuss tableaux for the Implicational Propositional Calculus and show how they may be used to establish its completeness.
We present equivalents to the Peirce axiom scheme and highlight its relevance for pairwise suprema.
We present a proof of completeness for the implicational propositional calculus, based on a variant of the Lindenbaum procedure.
We offer streamlined proofs of fundamental theorems regarding the index theory for partial self-maps of an infinite set that are bijective between cofinite subsets.
We investigate two ways in which self-maps of an infinite set may be close to bijections; our investigation generates a $\mathbb{Z}$-valued index theory and a corresponding extension by $\mathbb{Z}$ for the quotient of the full symmetric group by its finitary subgroup.
We investigate an `assumption of projectivity' that is appropriate to the self-dual axiomatic formulation of three-dimensional projective space.