Joost J. Joosten

Turing progressions and their well-orders

We see how Turing progressions are closely related to the closed fragment of GLP, polymodal provability logic. Next we study natural well-orders in GLP that characterize certain aspects of these Turing progressions.

Hyperations, Veblen progressions and transfinite iteration of ordinal functions

In this paper we introduce hyperations and cohyperations, which are forms of transnite iteration of ordinal functions. Hyperations are iterations of normal functions. Unlike iteration by pointwise convergence, hyperation preserves normality. The hyperationhf i 2On of a normal function f is a sequence of normal functions so that f 0 = id, f 1 = f and for all ; we have that f + = f f . These conditions do not determine f uniquely; in addition, we require thathf i 2On be minimal in an appropriate sense. We study hyperations systematically and show that they are a natural renement of Veblen progressions. Next, we dene cohyperations, very similar to hyperations except that they are left-additive: given ; , f + = f f . Cohyperations iterate initial functions which are functions that map initial segments to initial segments. We systematically study co-hyperations and see how they can be employed to dene left inverses to hyperations. Hyperations provide an alternative presentation of Veblen progressions and can be useful where a more ne-grained analysis of such sequences is

Well-orders in the transfinite Japaridze algebra

This paper studies the transfinite propositional provability logics

On the Necessity of Complexity

glp_Lambda

Hidden variables simulating quantum contextuality increasingly violate the Holevo bound

and their corresponding algebras. These logics have for each ordinal

Turing–Taylor Expansions for Arithmetic Theories

xi< Lambda

The Closed Fragment of IL is PSPACE Hard

a modality

The omega-rule interpretation of transfinite provability logic

la alpha ra

Turing Jumps Through Provability

. We will focus on the closed fragment of

Complexity Fits the Fittest

glp_Lambda