Related papers: Separating Maximality Principles
This paper continues the author's previous study \cite{Kura20}, showing that several weak principles inspired by non-normal modal logic suffice to derive various refined forms of the second incompleteness theorem. Among the main results of…
We give a brief survey on the interplay between forcing axioms and various other non-constructive principles widely used in many fields of abstract mathematics, such as the axiom of choice and Baire's category theorem. First of all we…
We consider the set M_n of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in M_n, we show that the upper canonical measure associated with…
With the help of various square principles, we obtain results concerning the consistency strength of several statements about trees containing ascent paths, special trees, and strong chain conditions. Building on a result that shows that…
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
We establish a majorization-based theory for bounding observables of waves with varied coherence. For any measurement, exact bounds are attained by the maximal and minimal elements in the set of input coherence spectra. The set's supremum…
Let $\Gamma$ be a non-uniform lattice in $PU(p,1)$ without torsion and with $p\geq2 $. We introduce the notion of volume for a representation $\rho:\Gamma \rightarrow PU(m,1)$ where $m \geq p$. We use this notion to generalize the…
In this paper we prove a strong maximum principle for certain parabolic systems of equations. In particular, our methods place no restriction on the regularity of the boundary of the convex set in which the system takes its values, and…
We provide, for any regular uncountable cardinal $\kappa$, a new argument for Pincus' result on the consistency of $\mathrm{ZF}$ with the higher dependent choice principle $\mathrm{DC}_{<\kappa}$ and the ordering principle in the presence…
An irredundant base of a group $G$ acting faithfully on a finite set $\Gamma$ is a sequence of points in $\Gamma$ that produces a strictly descending chain of pointwise stabiliser subgroups in $G$, terminating at the trivial subgroup.…
We study existence and uniqueness of invariant probability measures for continuous-time Markov processes on general state spaces. Existence is obtained from tightness of time averages under a weak regularity assumption inspired by…
We consider compactness characterizations of large cardinals. Based on results of Benda \cite{b-sccomp}, we study compactness for omitting types in various logics. In $\bL_{\kappa, \kappa}$, this allows us to characterize any large cardinal…
In this article we find necessary and sufficient conditions for the strong maximum principle and compact support principle for non-negative solutions to the quasilinear elliptic inequalities $$\Delta_\infty u + G(|Du|) - f(u)\,\leq 0\quad…
We prove a variation of Easton's lemma for strongly proper forcings, and use it to prove that, unlike the stronger principle $\textsf{IGMP}$, $\textsf{GMP}$ together with $2^\omega \le \omega_2$ is consistent with the existence of an…
In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal $\nu$ such that the singular cardinal hypothesis fails at $\nu$ and every collection of fewer than $\mathrm{cf}(\nu)$…
We use the core model for sequences of measures to prove a new lower bound for the consistency strength of the failure of the SCH: THEOREM (i) If there is a singular strong limit cardinal $\kappa$ such that $2^\kappa > kappa^+$ then there…
In this paper we generalize the main result of [4] for manifolds that are not necessarily Einstein. In fact, we obtain an upper bound for the volume of a locally volume-minimizing closed hypersurface $\Sigma$ of a Riemannian 5-manifold $M$…
The Necessary Maximality Principle for c.c.c. forcing asserts that any statement about a real in a c.c.c. extension that could become true in a further c.c.c. extension and remain true in all subsequent c.c.c. extensions, is already true in…
Assuming the P-ideal dichotomy, we attempt to isolate those cardinal characteristics of the continuum that are correlated with two well-known consequences of the proper forcing axiom. We find a cardinal invariant $\mathfrak{x}$ such that…
This work is a part of my upcoming thesis [7]. We establish an equiconsistency between (1) weak indestructibility for all $\kappa +2$-degrees of strength for cardinals $\kappa $ in the presence of a proper class of strong cardinals, and (2)…