In this paper, we present set theories based upon the paraconsistent logic Pac. We describe two different techniques to construct models of such set theories. The first of these is an adaptation of one used to construct classical models of positive comprehension. The properties of the models obtained in that way give rise to a natural paraconsistent set theory which is presented here. The status of the axiom of choice in that theory is also discussed. The second leads to show (...) that any classical universe of set theory (e.g. a model of ZF) can be extended to a paraconsistent one, via a term model construction using an adapted bisimulation technique. (shrink)

This paper is concerned with topological set theory, and particularly with Skala's and Manakos' systems for which we give a topological characterization of the models. This enables us to answer natural questions about those theories, reviewing previous results and proving new ones. One of these shows that Skala's set theory is in a sense compatible with any ‘normal’ set theory, and another appears on the semantic side as a ‘Cantor theorem’ for the category of Alexandroff spaces.

We show that the untyped λ -calculus can be extended with Frege's interpretation of propositional notions, provided we restrict β -conversion to positive expressions. The system of illative λ -calculus so obtained admits a natural Scott-style semantics.

It is proved in this paper that the positive abstraction scheme is consistent with extensionality only if one drops equality out of the language. The theory obtained is then compared with GPK, a wellknown set theory based on an extended positive comprehension scheme.

In this paper, we hypothesize that X chromosome-associated mechanisms, which affect X-linked genes and are behind the immunological advantage of females, may also affect X-linked microRNAs. The human X chromosome contains 10% of all microRNAs detected so far in the human genome. Although the role of most of them has not yet been described, several X chromosome-located microRNAs have important functions in immunity and cancer. We therefore provide a detailed map of all described microRNAs located on human and mouse X (...) chromosomes, and highlight the ones involved in immune functions and oncogenesis. The unique mode of inheritance of the X chromosome is ultimately the cause of the immune disadvantage of males and the enhanced survival of females following immunological challenges. How these aspects influence X-linked microRNAs will be a challenge for researchers in the coming years, not only from an evolutionary point of view, but also from the perspective of disease etiology. (shrink)

Journal Name: Semiotica Issue: Ahead of print.

We present an order-theoretic analysis of set-theoretic paradoxes. This analysis will show that a large variety of purely set-theoretic paradoxes (including the various Russell paradoxes as well as all the familiar implementations of the paradoxes of Mirimanoff and Burali-Forti) are all instances of a single limitative phenomenon.

We state the consistency problem of extensional partial set theory and prove two complementary results toward a definitive solution. The proof of one of our results makes use of an extension of the topological construction that was originally applied in the paraconsistent case.