APAL
2005
13 years 11 months ago
2005
We give a broad discussion of reflection principles in explicit mathematics, thereby addressing various kinds of universe existence principles. The proof-theoretic strength of the...
APAL
2005
13 years 11 months ago
2005
APAL
2005
13 years 11 months ago
2005
Abstract. Let n be a positive integer and FA (n) be the free abelian latticeordered group on n generators. We prove that FA (m) and FA (n) do not satisfy the same first-order sente...
APAL
2005
13 years 11 months ago
2005
In this paper we consider distributive modal logic, a setting in which we may add modalities, such as classical types of modalities as well as weak forms of negation, to the fragm...
APAL
2005
13 years 11 months ago
2005
The class of geometric surgical theories (which includes all o-minimal theories) is examined. The main theorem is that every stable theory that is interpretable in a geometric sur...
APAL
2005
13 years 11 months ago
2005
A new semantics is presented for the logic of proofs (LP), [1, 2], based on the intuition that it is a logic of explicit knowledge. This semantics is used to give new proofs of se...
APAL
2005
13 years 11 months ago
2005
Abstract. We construct a computable vector space with the trivial computable automorphism group, but with the dependence relations as complicated as possible, measured by their Tur...
APAL
2005
13 years 11 months ago
2005
Let A [] be a maximal almost disjoint family and assume P is a forcing notion. Say A is P-indestructible if A is still maximal in any P-generic extension. We investigate P-indest...
APAL
2005
13 years 11 months ago
2005
APAL
2005
13 years 11 months ago
2005
We investigate operators which take a set X to a set relatively computably enumerable in and above X by studying which such sets X can be so mapped into the Turing degree of K. We...