APAL
2007
13 years 11 months ago
2007
It is possible to control to a large extent, via semiproper forcing, the parameters (β0, β1) measuring the guessing density of the members of any given antichain of stationary s...
APAL
2007
13 years 11 months ago
2007
Non-well-founded trees are used in mathematics and computer science, for modelling non-well-founded sets, as well as non-terminating processes or infinite data structures. Catego...
APAL
2007
13 years 11 months ago
2007
In this paper we consider a type system with a universal type ω where any term (whether open or closed, β-normalising or not) has type ω. We provide this type system with a rea...
APAL
2007
13 years 11 months ago
2007
We give an exponential lower bound on number of proof-lines in intuitionistic propositional logic, IL, axiomatised in the usual Frege-style fashion; i.e., we give an example of IL...
APAL
2007
13 years 11 months ago
2007
We show that there exists a real α such that, for all reals β, if α is linear reducible to β (α ≤ β, previously denoted α ≤sw β) then β ≤T α. In fact, every random ...
APAL
2007
13 years 11 months ago
2007
In this article we study applications of the bounded functional interpretation to theories of feasible arithmetic and analysis. The main results show that the novel interpretation...
APAL
2007
13 years 11 months ago
2007
I modify the standard coverage construction of the reals to obtain the irrationals. However, this causes a jump in ordinal complexity from ω + 1 to Ω. The coverage technique ha...
APAL
2007
13 years 11 months ago
2007
A logic is developed in which function symbols are allowed to represent partial functions. It has the usual rules of logic (in the form of a sequent calculus) except that the subs...
APAL
2007
13 years 11 months ago
2007
We prove that, if V is an effectively given commutative valuation domain such that its value group is dense and archimedean, then the theory of all V -modules is decidable.