Abstract We show that a $(\kappa ^{+},1)$ -simplified morass can be added by a forcing with working parts of size smaller than $\kappa $ . This answers affirmatively the question, asked independently by Shelah and Velleman in the early 1990s, of whether it is possible to do so. Our argument use a modification of a technique of Mitchell’s for adding objects of size $\omega _2$ in which collections of models – all of equal, countable size – are used as side conditions. In our modification, whilst the individual models are, as in Mitchell’s technique, taken ad hoc from quite general classes, the collections of models are very highly structured, in a way that is somewhat different from, perhaps more stringent than, Mitchell’s original, arguably making the method more wieldy and giving the prospect of further uses with more delicate working parts.

We prove that it is consistent that $\aleph_\omega$ is strong limit, $2^{\aleph_\omega}$ is large and the universality number for graphs on $\aleph_{\omega+1}$ is small. The proof uses Prikry forcing with interleaved collapsing.

In fast-transcribing prokaryotic genes, such as an rrn gene in Escherichia coli, many RNA polymerases (RNAPs) transcribe the DNA simultaneously. Active elongation of RNAPs is often interrupted by pauses, which has been observed to cause RNAP traffic jams; yet some studies indicate that elongation seems to be faster in the presence of multiple RNAPs than elongation by a single RNAP. We propose that an interaction between RNAPs via the torque produced by RNAP motion on helically twisted DNA can explain this apparent paradox. We have incorporated the torque mechanism into a stochastic model and simulated transcription both with and without torque. Simulation results illustrate that the torque causes shorter pause durations and fewer collisions between polymerases. Our results suggest that the torsional interaction of RNAPs is an important mechanism in maintaining fast transcription times, and that transcription should be viewed as a cooperative group effort by multiple polymerases.

Abstract We prove consistent, assuming there is a supercompact cardinal, that there is a singular strong limit cardinalμ, of cofinalityω, such that everyμ+-chromatic graphXonμ+has an edge colouringcofXintoμcolours for which every vertex colouringgofXinto at mostμmany colours has ag-colour class on whichctakes every value. The paper also contains some generalisations of the above statement in whichμ+is replaced by other cardinals >μ.

Abstract This paper concerns the theory of morasses. In the early 1970s Jensen defined (k, α)-morasses for uncountable regular cardinals k and ordinals α < k. In the early 1980s Velleman defined (k, 1)-simplified morasses for all regular cardinals k. He showed that there is a (k, 1)-simplified morass if and only if there is (k, 1)-morass. More recently he defined (k, 2)-simplified morasses and Jensen was able to show that if there is a (k, 2)-morass then there is a (k, 2)-simplified morass. In this paper we prove the converse of Jensen's result, i.e., that if there is a (k, 2)-simplified morass then there is a (k, 2)-morass.

Many AI researchers have come to be dissatisfied with approaches to their discipline based on formal logic. Various alternatives are often suggested, including probability theory. This paper investigates the intimate connection between probability theory and various logics. We show that probability theory, broadly conceived, may be used as a formal semantics for virtually any monotonic logic. Thus, rather than being seen as competing, it is more appropriate to view formal logics as very special cases of probability theory, usually special cases that are computationally more tractable than the more general theory. Thus, probability theory and logic should be seen as complementary. Viewing probability theory in this abstract way may help to shed light on various recalcitrant problems in AI. De nombreux chercheurs dans le domaine de l'intelligence artificielle manifestent une certaine insatisfaction vis‐à‐vis certaines approches basées sur la logique formelle. Diverses solutions sont souvent proposées, y compris la théorie des probabilityés. Cet article analyse la relation intime entre la théorie des probabilités et diverses logiques. Il est démontré que la théorie des probabilityés, conçue de manière générale, peut ětre utilisée comme une sémantique formelle pour presque toute logique monotonique. Au lieu de percevoir les logiques formelles comme étant en opposition, il est plus approprié de les considérer comme des cas trés spéciaux de la théorie des probabilityés, habituellement plus traitables au niveau calcul que la théorie plus générate. Par conséquent, la théorie des probabilityés et la logique doivent ětre percues comme des éléments complémentaires. Le fait de considérer la théorie des probabilityés d'une manière abstraite peut contribuer à la compréhension de divers problèmes ardus dans le domaine de l'intelligence artificielle.

In this paper we outline two basic methods for automated theorem proving in nonclassical logics, including modal, many-valued, relevance, and intuitionistic logics. We discuss advantages and disadvantages of each method and give several illustrative examples. We outline a procedure for attacking more complex problems using a combination of the two basic methods. Results of experimental applications of the techniques are reported.

Abstract The usual semantics for the modal systems T, S4, and S5 assumes that the set of possible worlds contains at least one member. Recently versions of these modal systems have been developed in which this assumption is dropped. The systems discussed here are obtained by slightly weakening the liberated versions of T and S4. The semantics does not assume the existence of possible worlds, and the accessibility relation between worlds is only required to be quasi-reflexive instead of reflexive. Completeness and independence results are established.