APAL
2005
13 years 4 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 4 months ago
2005
APAL
2005
13 years 4 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 4 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 4 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 4 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 4 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 4 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 4 months ago
2005
APAL
2005
13 years 4 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...