This paper investigates the notion of the maximality effect and its formal implementation. It will be shown that the maximal witness sets that an anaphor can access are sensitive to the plural readings of the anaphor’s antecedents. It will also be shown that the formal semantics of the maximality effect should not be implemented on the interpretation of either determiners or anaphors. Instead, ...

In this paper, we discuss some principles on the selection of the solutions of a special vectorial Hamilton-Jacobi system defined by (1.1) below. We first classify the equivalent solutions based on a wellknown construction and then discuss some selection principles using intuitive descriptions of coarseness or maximality of solutions. We also discuss a selection principle based on comparison of...

where Xt= jBtjp and St = max 0 r t jBrjp. In the case p=1 the closed form for s 7! g (s) is found. This yields 1;q = (q(q+1)=2)( (1+(q+1)=q)) for all q > 0 . In the case p 6= 1 no closed form for s 7! g (s) seems to exist. The inequality above holds also in the case p = q+1 (Doob’s maximal inequality ). In this case the equation above (with K = p=2c ) admits g (s) = s as the maximal solution, a...

We study the logical content of several maximality principles related to the finite intersection principle (F IP) in set theory. Classically, these are all equivalent to the axiom of choice, but in the context of reverse mathematics their strengths vary: some are equivalent to ACA0 over RCA0, while others are strictly weaker and incomparable with WKL0. We show that there is a computable instanc...

Hamkins and Löwe proved that the modal logic of forcing is S4.2. In this paper, we consider its modal companion, the intermediate logic KC and relate it to the fatal Heyting algebra HZFC of forcing persistent sentences. This Heyting algebra is equationally generic for the class of fatal Heyting algebras. Motivated by these results, we further analyse the class of fatal Heyting algebras.

We give a short proof of a lemma which generalizes both the main lemma from the original construction in the author’s thesis of a model with no ω2-Aronszajn trees, and also the “Key Lemma” in Hamkins’s gap forcing theorems. The new lemma directly yields Hamkins’s newer lemma stating that certain forcing notions have the approximation property. According to Hamkins [2], a partial ordering P sati...

This paper extends to process algebras the notion of maximality which has initially been introduced for prime event structures and P/T nets and shows how this notion of maximality may be used for deening an adequate semantics of Basic LOTOS able to support action reenement. Such an approach appears to be more convenient than the classical ST-semantics where non atomic actions are split into sta...

We consider the decision problem of whether or not a given regular language is maximal with respect to certain combined types of code properties. In the recent past, there have been a few formal methods for defining code properties, such as trajectory-based codes and transducer-based codes, that allow one to decide the maximality problem, including the case where maximality is tested with respe...