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APAL
2005
13 years 5 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 5 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 5 months ago
2005
Systems of explicit mathematics provide an axiomatic framework to represent programs and to prove properties of them. We introduce such a system with a new form of power types usi...
APAL
2005
13 years 5 months ago
2005
We prove that S4 is complete with respect to Boolean combinations of countable unions of convex subsets of the real line, thus strengthening a 1944 result of McKinsey and Tarski (...
APAL
2005
13 years 5 months ago
2005
We propose an extension of answer sets, that we call safe beliefs, that can be used to study several properties and notions of answer sets and logic programming from a more genera...