Related papers: The universal logic of repeated experiments

We study conditions on automorphisms of Boolean algebras of the form $P(\lambda)/I_\kappa$ (where $\lambda$ is an uncountable cardinal and $I_\kappa$ is the ideal of sets of cardinality less than $\kappa$) which allow one to conclude that a…

We introduce a natural generalization of Borel's Conjecture. For each infinite cardinal number $\kappa$, let {\sf BC}$_{\kappa}$ denote this generalization. Then ${\sf BC}_{\aleph_0}$ is equivalent to the classical Borel conjecture.…

It is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. This contrasts with the case of the full elementary theory of the finitely generated free…

This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\em Boolean algebra of…

We prove that any suitable generalization of Laver forcing to the space $ \kappa^\kappa$, for uncountable regular $\kappa$, necessarily adds a Cohen $\kappa$-real. We also study a dichotomy and an ideal naturally related to generalized…

For the first time it is shown that the logic of quantum mechanics can be derived from Classical Physics. An orthomodular lattice of propositions, characteristic of quantum logic, is constructed for manifolds in Einstein's theory of general…

The logic $\mathcal L^1_\kappa$ was introduced by Shelah in [3]. In [4], he proved that for a strongly compact cardinal $\kappa$, it admits the following algebraic characterization: two structures are $\mathcal L^1_\kappa$-equivalent if and…

For a cardinal of the form $\kappa=\beth_\kappa$, Shelah's logic $L^1_\kappa$ has a characterisation as the maximal logic above $\bigcup_{\lambda<\kappa} L_{\lambda, \omega}$ satisfying Strong Undefinability of Well Order (SUDWO). SUDWO is…

For every algebraic number $\kappa$ on the unit circle which is not a root of unity we prove the existence of a strict sequence of algebraic numbers whose height tends to zero, such that the averages of the evaluation of $f_\kappa(z)=\log|z…

In this paper we study the Borel reducibility of Borel equivalence relations, including some orbit equivalence relations, on the generalised Baire space $\kappa^\kappa$ for an uncountable $\kappa$ with the property…

We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space. We give an equivalent proof for the classical…

The fundamental algebraic concepts of quantum mechanics, as expressed by many authors, are reviewed and translated into the framework of the relatively new non-distributive system of Boolean fractions (also called conditional events or…

We argue that the notion of epistemic \emph{possible worlds} in constructivism (intuitionism) is not as the same as it is in classic view, and there are possibilities, called non-predetermined worlds, which are ignored in (classic)…

Assuming a large cardinal hypothesis, Laver gave a representation of the monogenerated free left distributive algebra (LDA) using elementary embeddings and used this representation to prove many algebraic results. Some of these results were…

Universal continuous calculi are defined and it is shown that for every finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an ordered *-algebra that is symmetric, i.e. "strictly" positive elements are invertible, and…

A stationary subset $S$ of a regular uncountable cardinal $\kappa$ {\it reflects fully} at regular cardinals if for every stationary set $T \subseteq \kappa$ of higher order consisting of regular cardinals there exists an $\alpha \in T$…

Motivated by recent results and questions of D. Raghavan and S. Shelah, we present ZFC theorems on the bounding and various almost disjointness numbers, as well as on reaping and dominating families on uncountable, regular cardinals. We…

In this paper, some features of countably $\alpha$-compact topological spaces are presented and proven. The connection between countably $\alpha$% -compact, Tychonoff, and $\alpha$-Hausdorff spaces is explained. The space is countably…

Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad…

All spaces are assumed to be infinite Hausdorff spaces. We call a space "anti-Urysohn" $($AU in short$)$ iff any two non-emty regular closed sets in it intersect. We prove that $\bullet$ for every infinite cardinal ${\kappa}$ there is a…