Elementary Complexity into the Hyperfinite II1 Factor
نویسندگان
چکیده
In this paper, we show how the framework of von Neumann algebras can be applied to model the dynamics of computational processes. Namely, our aim is to gain an understanding of classical computation in terms of the hyperfinite factor, starting from the class of Kalmar recursive functions. Our model fits within a vast project of reshaping the unified theory of semantics of computation called geometry of interaction along the lines recently sketched by J.Y. Girard.
منابع مشابه
Computability and the Connes Embedding Problem
The Connes Embedding Problem (CEP) asks whether every separable II1 factor embeds into an ultrapower of the hyperfinite II1 factor. We show that the CEP is equivalent to the statement that every type II1 tracial von Neumann algebra has a computable universal theory.
متن کاملDirichlet forms on hyperfinite II1 factor
Based on the structure of the hyperfinite II1 factor, we study its Dirichlet forms which can be constructed from Dirichlet forms on M2n(C).
متن کاملA continuous path of singular masas in the hyperfinite II1 factor
Using methods of R.J.Tauer [13] we exhibit an uncountable family of singular masas in the hyperfinite II1 factor R all with Pukánszky invariant {1}, no pair of which are conjugate by an automorphism of R. This is done by introducing an invariant Γ(A) for a masa A in a II1 factor N as the maximal size of a projection e ∈ A for which Ae contains non-trivial centralising sequences for eNe. The mas...
متن کاملConnes’ Embedding Problem and Lance’s Wep
A II1-factor embeds into the ultraproduct of the hyperfinite II1-factor if and only if it satisfies the von Neumann algebraic analogue of Lance’s weak expectation property (WEP). This note gives a self contained proof of this fact.
متن کاملSome Quasinilpotent Generators of the Hyperfinite Ii1 Factor
Abstract. For each sequence {cn}n in l1(N) we define an operator A in the hyperfinite II1-factor R. We prove that these operators are quasinilpotent and they generate the whole hyperfinite II1-factor. We show that they have non-trivial, closed, invariant subspaces affiliated to the von Neumann algebra and we provide enough evidence to suggest that these operators are interesting for the hyperin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007