Jita Glide Epenthesis and the Maximality Principle

On Foreman's Maximality Principle

In this paper we consider Foreman’s maximality principle, which says that any non-trivial forcing notion either adds a new real or collapses some cardinals. We prove the consistency of some of its consequences. We observe that it is consistent that every c.c.c. forcing adds a real and that for every uncountable regular cardinal κ, every κ-closed forcing of size 2<κ collapses some cardinal.

A simple maximality principle

In this paper, following an idea of Christophe Chalons, I propose a new kind of forcing axiom, the Maximality Principle, which asserts that any sentence φ holding in some forcing extension V P and all subsequent extensions V P∗Q̇ holds already in V . It follows, in fact, that such sentences must also hold in all forcing extensions of V . In modal terms, therefore, the Maximality Principle is exp...

Optimal Stopping of the Maximum Process: The Maximality Principle

where S = (St)t 0 is the maximum process associated with the one-dimensional time-homogeneous diffusion X = (Xt)t 0 , the function x 7! c(x) is positive and continuous, and the supremum is taken over all stopping times of X for which the integral has finite expectation. It is proved, under no extra conditions, that this problem has a solution, i.e. the payoff is finite and there is an optimal s...

Coronal epenthesis and markedness

The Necessary Maximality Principle for c. c. c. forcing is equiconsistent with a weakly compact cardinal

The Necessary Maximality Principle for c.c.c. forcing with real parameters is equiconsistent with the existence of a weakly compact cardinal. The Necessary Maximality Principle for c.c.c. forcing, denoted 2mpccc(R), 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 tr...