where the surfaces f∗ and g∗ can be characterised as extremal solutions to a couple of first-order nonlinear PDEs expressed in terms of the infinitesimal characteristics of X and c . This is done by extending the arguments associated with the maximality principle [29] to the three-dimensional setting of the present problem and disclosing the general structure of the solution that is valid in al...

‎We present streamlined proofs of certain maximality principles studied by Hamkins‎ ‎and Woodin‎. ‎Moreover‎, ‎we formulate an intermediate maximality principle‎, ‎which is‎ ‎shown here to be equiconsistent with the existence of a weakly compact cardinal $kappa$ such that $V_{kappa}prec V$‎.

This paper reports completeness results for dyadic deontic logics in the tradition of Hansson’s systems. There are two ways to understand the core notion of best antecedentworlds, which underpins such systems. One is in terms of maximality, and the other in terms of optimality. Depending on the choice being made, one gets different evaluation rules for the deontic modalities, but also different...

The author establishes a connection between Revision Theory of Truth and Infinite Time Turing Machines as developed by Hamkins and Kidder. The ideas from this paper have incited Welch to solve the limit rule problem of revision theory.

We continue the study of tall cardinals and related notions begun by Hamkins in [11] and answer three of his questions posed in that paper.

We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove strong necessary optimality condition of Pontryagin type. The possibility that admissible are subject to pointwise constraints is new requires more sophisticated techniques include maximality condition. start by proving results continuity solutions due needle-like pe...

This paper is an attempt at a synthesis of two superficially conflicting approaches to non-maximality: the issue-based approach (Malamud 2012, Križ 2015, & Spector 2021 a.o.), which generates clear-cut truth conditions once issue parameter has been fixed, and strict/tolerant (Burnett 2017 on non-maximal construals involve vagueness. I argue that there are classes contexts license non-maxima...

Ever since the rise of non-standard models and the proliferation of the independence results there have been two conflicting positions in the foundations of mathematics. The first position—which we shall call pluralism—maintains that certain statements of mathematics do not have determinate truth-values. On this view, although it is admitted that there are are practical reasons that one might g...

We define a potentialist system of ZF-structures, that is, collection possible worlds in the language ZF connected by binary accessibility relation, achieving account full background set-theoretic universe $V$. The definition involves Berkeley cardinals, strongest known large cardinal axioms, inconsistent with Axiom Choice. In fact, as theory we assume just ZF. It turns out propositional modal ...