We prove that if Q is a nw-nep forcing then it cannot add a dominating real. We also show that amoeba forcing cannot be P(X)/I if I is an א1-complete ideal. Furthermore, we generalize the results of [12].

There is a partial order P preserving stationary subsets of !1 and forcing that every partial order in the ground model V that collapses a su ciently large ordinal to !1 over V also collapses !1 over V P. The proof of this uses a coding of reals into ordinals by proper forcing discovered by Justin Moore and a symmetric extension of the universe in which the Axiom of Choice fails. Also, using on...

We show that several weakenings of the Cauchy condition are all equivalent under the assumption of countable choice, and investigate to what extent choice is necessary. We also show that the syntactically reminiscent notion of metastability allows similar variations, but in terms of its computational content is an empty notion. §1. Almost Cauchyness. Apart from the last section, we work in Bish...

In this paper we consider a number of issues concerned with how creativity can exist within a paradigm of computational search. We look both at creativity within the search process and the capacity of the search space to facilitate creativity. Within the latter we consider notions of compressibility and openness in search spaces; the influence of modularity and substructures on creativity; and ...

We study and compare two notions of non-termination on idempotent semirings: infinite iteration and divergence. We determine them in various models and develop conditions for their coincidence. It turns out that divergence yields a simple and natural way of modelling infinite behaviour, whereas infinite iteration shows some anomalies.

The main result of this paper is a partial answer to [6, Problem 5.5]: a finite iteration of Universal Meager forcing notions adds generic filters for many forcing notions determined by universality parameters. We also give some results concerning cardinal characteristics of the σ–ideals determined by those universality parameters. One of the most striking differences between measure and catego...

We survey notions of aliasing and ownership. An extreme but conceptually useful model is that of pure linear languages where each object is constructed once and read, being consumed, once. We see more realistic programming languages as relaxing this to allow multiple references to an object (spatial aliasing) or multiple sequenced operations on a single live reference (temporal aliasing) before...

The bounded approximate version of $varphi$-amenability and character amenability are introduced and studied. These new notions are characterized in several different ways, and some hereditary properties of them are established. The general theory for these concepts is also developed. Moreover, some examples are given to show that these notions are different from the others. Finally, bounded ap...

There are hypotheses in the history of human culture and civilization in which we can find undeniable similarities and commonalities among them, despite their vastly different cultural and historical contexts. For example, finding commonalities between the language of two artistic aesthetic hypotheses, Sufism and Surrealism, which are very different from each other in terms of context, time as ...

The paper is devoted to concern a relationship between rough set theory and universal algebra. Notions of lower and upper rough approximations on an algebraic structure induced by an ideal are introduced and some of their properties are studied. Also, notions of rough subalgebras and rough ideals with respect to an ideal of an algebraic structure, which is an extended notion of subalgebras and ...