Dresner BOOLEAN ALGEBRAS AND NATURAL LANGUAGE : A MEASUREMENT THEORETIC

Boolean Algebras And Natural Language: A Measurement Theoretic Approach

Imaginaries in Boolean algebras

Given an infinite Boolean algebra B, we find a natural class of ∅-definable equivalence relations EB such that every imaginary element from B is interdefinable with an element from a sort determined by some equivalence relation from EB . It follows that B together with the family of sorts determined by EB admits elimination of imaginaries in a suitable multisorted language. The paper generalize...

Nonassociative Lambek Calculus with Additives and Context-Free Languages

We study Nonassociative Lambek Calculus with additives ∧,∨, satisfying the distributive law (Distributive Full Nonassociative Lambek Calculus DFNL). We prove that categorial grammars based on DFNL, also enriched with assumptions, generate context-free languages. The proof uses proof-theoretic tools (interpolation) and a construction of a finite model, earlier employed in [11] in the proof of Fi...

Boolean algebras, Stone spaces and TGD

The Facebook discussion with Stephen King about Stone spaces led to a highly interesting development of ideas concerning Boolean, algebras, Stone spaces, and p-adic physics. I have discussed these ideas already earlier but the improved understanding of the notion of Stone space helped to make the ideas more concrete. The basic ideas are briefly summarized. p-adic integers/numbers correspond to ...

Densities of Ultraproducts of Boolean Algebras

We answer three problems by J. D. Monk on cardinal invariants of Boolean algebras. Two of these are whether taking the algebraic density πA resp. the topological density dA of a Boolean algebra A commutes with formation of ultraproducts; the third one compares the number of endomorphisms and of ideals of a Boolean algebra. In set theoretic topology, considerable effort has been put into the stu...