Mathematical Papers


“Self-constructing continua” is the mathematical core of the Bergsonian axioms project; it should be accessible to anyone familiar with the boolean-algebraic approach to forcing (used in standard set-theory texts like T. Jech’s or J. L. Bell’s). It presents the Bergsonian axioms, argues that they capture the intuitive notion of a self-constructing mathematical universe, develops a forcing construction to produce candidate models of the axioms, and shows that the boolean algebras most commonly used for forcing do not work when used as inputs to this construction.

“AQFT as a possible source of self-constructing continua” shows that some models of algebraic quantum field theory would, assuming a Main Conjecture about the projection lattices of von Neumann subfactors, yield boolean algebras suitable as inputs to the forcing construction in “Self-constructing continua.”

This Main Conjecture is, alas, false, at least assuming the continuum hypothesis (CH): this is shown in “Under CH, the boolean completion of a type III factor’s projection lattice is the standard continuum-collapsing algebra.”

“Noncommutative analogs of random-real forcing” shows that random-real forcing is equivalent to using the projection lattice of a commutative von Neumann algebra to force a generic state on that algebra, and it shows that generic states will also be forced when the von Neumann algebra used is noncommutative.