2 citations · 4 across the 13 of their papers we have counts for
17 papers
Inconsistency of Reinhardt cardinals with
Rupert McCallum
A proof will be presented that the existence of a non-trivial -elementary embedding is inconsistent with . Sections 1 and 2 shall revie…
Brouwer fixed point theorem as a corollary of Lawvere
Rupert McCallum
It is investigated in what sense the Brouwer fixed point theorem may be viewed as a corollary of the Lawvere fixed point theorem. A suitable generalisation of the Lawvere fixed poi…
A proof of P!=NP
Rupert McCallum
We show that it is provable in PA that there is an arithmetically definable sequence of -sentences, such that - PRA+ is $Π^{0}_{2}…
New Large Cardinal Axioms and the Ultimate-L Program
Rupert McCallum
We will consider a number of new large-cardinal properties, the -tremendous cardinals for each limit ordinal , the hyper-tremendous cardinals, the -enormous cardinals fo…
All large-cardinal axioms not known to be inconsistent with ZFC are justified
Rupert McCallum
In other work we have outlined how, building on ideas of Welch and Roberts, one can motivate believing in the existence of supercompact cardinals. After making this observation we…
Which axioms of set theory are intrinsically justified?
Rupert McCallum
We recently formulated a new large-cardinal axiom of strength intermediate between a totally indescribable cardinal and an -Erdős cardinal, positing the existence of what we cal…
The choiceless cardinals are inconsistent
Rupert McCallum
We give a proof of the Kunen inconsistency in ZF.
A prime geodesic theorem for higher rank buildings
Anton Deitmar, Rupert McCallum
We prove a prime geodesic theorem for compact quotients of affine buildings and apply it to get class number asymptotics for global fields of positive characteristic.
Twisted Poincare Series and Zeta functions on finite quotients of buildings
Ming-Hsuan Kang, Rupert McCallum
In the case where SL for a non-archimedean local field and is a discrete torsion-free cocompact subgroup of , there is a known relationship between the Ihar…
Height growth on semisimple groups
Anton Deitmar, Rupert McCallum
A condition is given, under which a general lattice point counting function is asymptotic to the corresponding ball volume growth function. This is then used to give height asympto…
Building lattices and zeta functions
Anton Deitmar, Ming-Hsuan Kang, Rupert McCallum
We introduce the notion of a building lattice generalizing tree lattices. We give a Lefschetz formula and apply it to geometric zeta functions. We further generalize Bass's approac…
Free subgroups of special linear groups
Rupert McCallum
We present a proof of the following claim. Suppose that is an integer such that and that is any field. Suppose that is an element of of infinit…
Intrinsic justifications for large-cardinal axioms
Rupert McCallum
William Tait and Peter Koellner have written on the topic of which reflection principles are intrinsically justified. Phillip Welch and Sam Roberts have recently sought to motivate…
Rigidity of the group topology for closed Weyl transitive groups of automorphisms of a regular locally finite building
Rupert McCallum
We prove that if is a group of automorphisms of a regular locally finite building which is closed in the compact-open topology and acts Weyl transitively on the building, then…
Topological rigidity in totally disconnected locally compact groups
Rupert McCallum
In \cite{Kramer11} Kramer proves for a large class of semisimple Lie groups that they admit just one locally compact -compact Hausdorff topology compatible with the group operat…
A Local-to-Global Result for Topological Spherical Buildings
Rupert McCallum
Suppose that Δ, Δ' are two buildings each arising from a semisimpe algebraic group over a field, a topological field in the former case, and that for both the buildings the Coxeter…
A Consistency Proof for Some Restrictions of Tait's Reflection Principles
Rupert McCallum
A new large-cardinal property is introduced which enables one to give a relative consistency proof of restricted versions of the reflection principles discussed by Tait in his essa…