APAL
2010
13 years 11 months ago
2010
We prove the strong normalization of full classical natural deduction (i.e. with conjunction, disjunction and permutative conversions) by using a translation into the simply typed...
APAL
2010
13 years 11 months ago
2010
We introduce a notion of Kripke model for classical logic for which we constructively prove soundness and cut-free completeness. We discuss the meaning of the new notion and its a...
APAL
2010
13 years 11 months ago
2010
A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTT0 and LTT 0, which we...
APAL
2010
13 years 11 months ago
2010
In this paper we define a notion of relativization for higher order logic. We then show that there is a higher order theory of Grothendieck topoi such that all Grothendieck topoi ...
APAL
2010
13 years 11 months ago
2010
We introduce a new and general notion of canonical extension for algebras in the algebraic counterpart AlgS of any finitary and congruential logic S. This definition is logic-base...
APAL
2010
13 years 11 months ago
2010
Using almost disjoint coding we prove the consistency of the existence of a 1 2 definable -mad family of infinite subsets of (resp. functions from to ) together with b = 2 = 2.
APAL
2010
13 years 11 months ago
2010
First order reasoning about hyperintegers can prove things about sets of integers. In the author's paper Nonstandard Arithmetic and Reverse Mathematics, Bulletin of Symbolic L...
APAL
2010
13 years 11 months ago
2010
APAL
2010
13 years 11 months ago
2010
We analyze the degree-structure induced by large reducibilities under the Axiom of Determinacy. This generalizes the analysis of Borel reducibilities given in [1], [6] and [5] e.g...
APAL
2010
13 years 11 months ago
2010
