THE SET-THEORETIC MULTIVERSE

Topos-theoretic Model of the Deutsch multiverse

The Deutsch multiverse is collection of parallel universes. In this article a formal theory and a topos-theoretic model of the Deutsch multiverse are given. For this the LawvereKock Synthetic Differential Geometry and topos models for smooth infinitesimal analysis are used. Physical properties of multi-variant and many-dimensional parallel universes are discussed. Quantum fluctuations of univer...

Multiverse conceptions in set theory

We review different conceptions of the set-theoretic multiverse and evaluate their features and strengths. In Section 1, we set the stage by briefly discussing the opposition between the ‘universe view’ and the ‘multiverse view’. Furthermore, we propose to classify multiverse conceptions in terms of their adherence to some form of mathematical realism. In Section 2, we use this classification t...

Multiverse Set Theory and Absolutely Undecidable Propositions

Order-theoretic Invariants in Set-theoretic Topology

We present several results related to van Douwen’s Problem, which asks whether there is homogeneous compactum with cellularity exceeding c, the cardinality of the reals. For example, just as all known homogeneous compacta have cellularity at most c, they satisfy similar upper bounds in terms of Peregudov’s Noetherian type and related cardinal functions defined by order-theoretic base properties...

Set Theoretic Real Analysis

This article is a survey of the recent results that concern real functions (from R into R) and whose solutions or statements involve the use of set theory. The choice of the topics follows the author’s personal interest in the subject, and there are probably some important results in this area that did not make it to this survey. Most of the results presented here are left without proofs. 1991 ...